Transactions of the American Mathematical Society最新文献_第9页

2区数学

Transactions of the American Mathematical Society Pub Date : 2023-11-09 DOI: 10.1090/tran/8996

Gabriel Islambouli, Patrick Naylor

{"title":"Multisections of 4-manifolds","authors":"Gabriel Islambouli, Patrick Naylor","doi":"10.1090/tran/8996","DOIUrl":"https://doi.org/10.1090/tran/8996","url":null,"abstract":"We introduce multisections of smooth, closed 4-manifolds, which generalize trisections to decompositions with more than three pieces. This decomposition describes an arbitrary smooth, closed 4-manifold as a sequence of cut systems on a surface. We show how to carry out many smooth cut and paste operations in terms of these cut systems. In particular, we show how to implement a cork twist, whereby we show that an arbitrary exotic pair of smooth 4-manifolds admit 4-sections differing only by one cut system. By carrying out fiber sums and log transforms, we also show that the elliptic fibrations <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E left-parenthesis n right-parenthesis Subscript p comma q\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>n</mml:mi> <mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">E(n)_{p,q}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> all admit genus <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=\"application/x-tex\">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> multisections, and draw explicit diagrams for these manifolds.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":" 30","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Products of normal subsets 正规子集的积

2区数学

Transactions of the American Mathematical Society Pub Date : 2023-11-08 DOI: 10.1090/tran/8960

Michael Larsen, Aner Shalev, Pham Tiep

引用次数: 0

Automorphisms and derivations of affine commutative and PI-algebras 仿射交换代数和pi -代数的自同构和导数

2区数学

Transactions of the American Mathematical Society Pub Date : 2023-11-08 DOI: 10.1090/tran/9071

Oksana Bezushchak, Anatoliy Petravchuk, Efim Zelmanov

{"title":"Automorphisms and derivations of affine commutative and PI-algebras","authors":"Oksana Bezushchak, Anatoliy Petravchuk, Efim Zelmanov","doi":"10.1090/tran/9071","DOIUrl":"https://doi.org/10.1090/tran/9071","url":null,"abstract":"We prove analogs of A. Selberg’s result for finitely generated subgroups of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A u t left-parenthesis upper A right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>Aut</mml:mi> <mml:mo>⁡</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">operatorname {Aut}(A)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and of Engel’s theorem for subalgebras of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D e r left-parenthesis upper A right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>Der</mml:mi> <mml:mo>⁡</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">operatorname {Der}(A)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for a finitely generated associative commutative algebra <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A\"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=\"application/x-tex\">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> over an associative commutative ring. We prove also an analog of the theorem of W. Burnside and I. Schur about local finiteness of torsion subgroups of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A u t left-parenthesis upper A right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>Aut</mml:mi> <mml:mo>⁡</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">operatorname {Aut}(A)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":" 18","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135293557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the distribution of partial quotients of reduced fractions with fixed denominator 定分母约简分数部分商的分布

2区数学

Transactions of the American Mathematical Society Pub Date : 2023-11-08 DOI: 10.1090/tran/9065

Christoph Aistleitner, Bence Borda, Manuel Hauke

{"title":"On the distribution of partial quotients of reduced fractions with fixed denominator","authors":"Christoph Aistleitner, Bence Borda, Manuel Hauke","doi":"10.1090/tran/9065","DOIUrl":"https://doi.org/10.1090/tran/9065","url":null,"abstract":"In this paper, we study distributional properties of the sequence of partial quotients in the continued fraction expansion of fractions <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"a slash upper N\"> <mml:semantics> <mml:mrow> <mml:mi>a</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>N</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">a/N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding=\"application/x-tex\">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is fixed and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"a\"> <mml:semantics> <mml:mi>a</mml:mi> <mml:annotation encoding=\"application/x-tex\">a</mml:annotation> </mml:semantics> </mml:math> </inline-formula> runs through the set of mod <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding=\"application/x-tex\">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> residue classes which are coprime with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding=\"application/x-tex\">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Our methods cover statistics such as the sum of partial quotients, the maximal partial quotient, the empirical distribution of partial quotients, Dedekind sums, and much more. We prove a sharp concentration inequality for the sum of partial quotients, and sharp tail estimates for the maximal partial quotient and for Dedekind sums, all matching the tail behavior in the limit laws which are known under an extra averaging over the set of possible denominators <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding=\"application/x-tex\">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that the distribution of partial quotients of reduced fractions with fixed denominator gives a very good fit to the Gauß–Kuzmin distribution. As corollaries we establish the existence of reduced fractions with a small sum of partial quotients resp. a small maximal partial quotient.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":" 17","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135293558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dihedral rigidity in hyperbolic 3-space 双曲三维空间中的二面体刚度

2区数学

Transactions of the American Mathematical Society Pub Date : 2023-11-08 DOI: 10.1090/tran/9057

Xiaoxiang Chai, Gaoming Wang

引用次数: 0

On linear stochastic flows 关于线性随机流

2区数学

Transactions of the American Mathematical Society Pub Date : 2023-11-08 DOI: 10.1090/tran/8782

Beniamin Goldys, Szymon Peszat

{"title":"On linear stochastic flows","authors":"Beniamin Goldys, Szymon Peszat","doi":"10.1090/tran/8782","DOIUrl":"https://doi.org/10.1090/tran/8782","url":null,"abstract":"We study the existence of the stochastic flow associated to a linear stochastic evolution equation <disp-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal d upper X equals upper A upper X normal d t plus sigma-summation Underscript k Endscripts upper B Subscript k Baseline upper X normal d upper W Subscript k Baseline comma\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"normal\">d</mml:mi> <mml:mo>⁡</mml:mo> <mml:mi>X</mml:mi> <mml:mo>=</mml:mo> <mml:mi>A</mml:mi> <mml:mi>X</mml:mi> <mml:mi mathvariant=\"normal\">d</mml:mi> <mml:mo>⁡</mml:mo> <mml:mi>t</mml:mi> <mml:mo>+</mml:mo> <mml:munder> <mml:mo>∑</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>k</mml:mi> </mml:mrow> </mml:munder> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mi>X</mml:mi> <mml:mi mathvariant=\"normal\">d</mml:mi> <mml:mo>⁡</mml:mo> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mo>,</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">begin{equation*} operatorname {d} X= AXoperatorname {d} t +sum _{k} B_k Xoperatorname {d} W_k, end{equation*}</mml:annotation> </mml:semantics> </mml:math> </disp-formula> on a Hilbert space. Our first result covers the case where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A\"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=\"application/x-tex\">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the generator of a <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C 0\"> <mml:semantics> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:annotation encoding=\"application/x-tex\">C_0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-semigroup, and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper B Subscript k Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(B_k)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a sequence of bounded linear operators such that <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"sigma-summation Underscript k Endscripts double-vertical-bar upper B Subscript k Baseline double-vertical-bar greater-than plus normal infinity\"> <mml:semantics> <mml:mrow> <mml:munder> <mml:mo>∑</mml:mo> <mml:mi>k</mml:mi> </mml:munder> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mo fence=\"false\" stretchy=\"false\">‖</mml:mo> <mml:mo>></mml:mo> <mml","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":" 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Holomorphic Hörmander-type functional calculus on sectors and strips 全纯Hörmander-type扇形和条形上的泛函演算

2区数学

Transactions of the American Mathematical Society Pub Date : 2023-11-03 DOI: 10.1090/btran/164

Markus Haase, Florian Pannasch

{"title":"Holomorphic Hörmander-type functional calculus on sectors and strips","authors":"Markus Haase, Florian Pannasch","doi":"10.1090/btran/164","DOIUrl":"https://doi.org/10.1090/btran/164","url":null,"abstract":"In this paper, the abstract multiplier theorems for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"0\"> <mml:semantics> <mml:mn>0</mml:mn> <mml:annotation encoding=\"application/x-tex\">0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-sectorial and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"0\"> <mml:semantics> <mml:mn>0</mml:mn> <mml:annotation encoding=\"application/x-tex\">0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-strip type operators by Kriegler and Weis [Math. Z. 289 (2018), pp. 405–444] are refined and generalized to arbitrary sectorial and strip-type operators. To this end, holomorphic Hörmander-type functions on sectors and strips are introduced, with even a finer scale of smoothness than the classical polynomial scale. Moreover, we establish alternative descriptions of these spaces involving Schwartz and “holomorphic Schwartz” functions. Finally, the abstract results are combined with a result by Carbonaro and Dragičević [Duke Math. J. 166 (2017), pp. 937–974] to obtain an improvement—with respect to the smoothness condition—of the known Hörmander-type multiplier theorem for general symmetric contraction semigroups.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"33 16","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135819028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Prognostic Utility of Left Atrial Strain to Predict Thrombotic Events and Mortality in Amyloid Cardiomyopathy. 左心房应变对预测淀粉样心肌病血栓事件和死亡率的预后作用

IF 14 2区数学

Transactions of the American Mathematical Society Pub Date : 2023-11-01 Epub Date: 2023-04-12 DOI: 10.1016/j.jcmg.2023.01.015

Emmanuel Akintoye, Muhammad Majid, Allan L Klein, Mazen Hanna

{"title":"Prognostic Utility of Left Atrial Strain to Predict Thrombotic Events and Mortality in Amyloid Cardiomyopathy.","authors":"Emmanuel Akintoye, Muhammad Majid, Allan L Klein, Mazen Hanna","doi":"10.1016/j.jcmg.2023.01.015","DOIUrl":"10.1016/j.jcmg.2023.01.015","url":null,"abstract":"Background: There is currently no thromboembolic risk stratification tool for amyloid cardiomyopathy (ACM) and the current survival staging systems for ACM have only modest discriminatory ability.Objectives: This study aims to evaluate the prognostic value of left atrial (LA) strain to predict incident thrombotic event (TE) and improve survival staging systems in ACM.Methods: The authors identified patients with light chain (AL) or transthyretin (ATTR) ACM and no history of atrial fibrillation (AF) at diagnosis. Three components of LA strain (reservoir, conduit, and contractile) were measured and their predictive value for TE and mortality was determined. In addition, the authors evaluated the incremental utility of adding LA strain to current prognostic staging systems.Results: The authors included 448 patients (50.2% AL; 49.8% ATTR) with median follow-up of 3.8 years. There were 64 (14.3%) TE cases, 103 (23%) AF cases, and 234 (52.2%) deaths. Notably, 75% of TEs occurred without preceding AF documented. LA strain reservoir and LA contractile strain significantly predicted both events: HRs for TE were 2.22 (95% CI: 1.27-3.85; P = 0.006) and 2.63 (95% CI: 1.25-5.00; P = 0.01) per SD decrease in LA strain reservoir and LA contractile strain, respectively. The respective HRs for mortality were 1.32 (95% CI: 1.09-1.59; P < 0.001) and 1.49 (95% CI: 1.22-1.75; P < 0.001). Also, LA strain reservoir and LA contractile strain significantly improved the C-statistics of the Mayo AL staging from 0.65 to 0.68 and 0.70, respectively (P ≤ 0.02); Mayo ATTR staging (0.73 to 0.79 and 0.80, respectively; P < 0.001); and Gillmore ATTR staging (0.70 to 0.79 and 0.80, respectively; P < 0.001).Conclusions: LA strain identifies ACM patients with high thrombotic risk (independent of AF) and improves current ACM-specific survival staging.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"354 1","pages":"1371-1383"},"PeriodicalIF":14.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82611840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

The continuity of 𝑝-rationality and a lower bound for 𝑝’-degree characters of finite groups 有限群的𝑝-rationality的连续性和𝑝′度特征的下界

2区数学

Transactions of the American Mathematical Society Pub Date : 2023-10-25 DOI: 10.1090/tran/8926

Nguyen Hung

{"title":"The continuity of 𝑝-rationality and a lower bound for 𝑝’-degree characters of finite groups","authors":"Nguyen Hung","doi":"10.1090/tran/8926","DOIUrl":"https://doi.org/10.1090/tran/8926","url":null,"abstract":"Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a prime and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a finite group. We propose a strong bound for the number of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p prime\"> <mml:semantics> <mml:msup> <mml:mi>p</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:annotation encoding=\"application/x-tex\">p’</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-degree irreducible characters of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in terms of the commutator factor group of a Sylow <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-subgroup of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The bound arises from a recent conjecture of Navarro and Tiep [Forum Math. Pi 9 (2021), pp. 1–28] on fields of character values and a phenomenon called the continuity of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-rationality level of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p prime\"> <mml:semantics> <mml:msup> <mml:mi>p</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:annotation encoding=\"application/x-tex\">p’</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-degree characters. This continuity property in turn is predicted by the celebrated McKay-Navarro conjecture (see G. Navarro [Ann. of Math. (2) 160 (2004), pp. 1129–1140]). We achieve both the bound and the continuity property for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p equals 2\"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> ","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"47 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134972239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Residual intersections and linear powers 剩余交集和线性幂

2区数学

Transactions of the American Mathematical Society Pub Date : 2023-10-23 DOI: 10.1090/btran/127

David Eisenbud, Craig Huneke, Bernd Ulrich

{"title":"Residual intersections and linear powers","authors":"David Eisenbud, Craig Huneke, Bernd Ulrich","doi":"10.1090/btran/127","DOIUrl":"https://doi.org/10.1090/btran/127","url":null,"abstract":"If <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I\"> <mml:semantics> <mml:mi>I</mml:mi> <mml:annotation encoding=\"application/x-tex\">I</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is an ideal in a Gorenstein ring <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S\"> <mml:semantics> <mml:mi>S</mml:mi> <mml:annotation encoding=\"application/x-tex\">S</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S slash upper I\"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>I</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">S/I</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is Cohen-Macaulay, then the same is true for any linked ideal <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I prime\"> <mml:semantics> <mml:msup> <mml:mi>I</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:annotation encoding=\"application/x-tex\">I’</mml:annotation> </mml:semantics> </mml:math> </inline-formula>; but such statements hold for residual intersections of higher codimension only under restrictive hypotheses, not satisfied even by ideals as simple as the ideal <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Subscript n\"> <mml:semantics> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding=\"application/x-tex\">L_{n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of minors of a generic <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2 times n\"> <mml:semantics> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">2 times n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> matrix when <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n greater-than 3\"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>></mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">n>3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In this paper we initiate the study of a different sort of Cohen-Macaulay property that holds for certain general residual intersections of the maximal (interesting) codimension, one less than the analytic spread of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I\"> <mml:semantics> <mml:mi>I</mml:mi> <mml:annotation encoding=\"app","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"724 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135322747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1