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CONSTRUCTING NONPROXY SMALL TEST MODULES FOR THE COMPLETE INTERSECTION PROPERTY 构造完全交性质的非xy小测试模块
IF 0.8 2区 数学
Nagoya Mathematical Journal Pub Date : 2020-09-24 DOI: 10.1017/nmj.2021.7
Benjamin Briggs, Eloísa Grifo, Josh Pollitz
{"title":"CONSTRUCTING NONPROXY SMALL TEST MODULES FOR THE COMPLETE INTERSECTION PROPERTY","authors":"Benjamin Briggs, Eloísa Grifo, Josh Pollitz","doi":"10.1017/nmj.2021.7","DOIUrl":"https://doi.org/10.1017/nmj.2021.7","url":null,"abstract":"Abstract A local ring R is regular if and only if every finitely generated R-module has finite projective dimension. Moreover, the residue field k is a test module: R is regular if and only if k has finite projective dimension. This characterization can be extended to the bounded derived category \u0000$mathsf {D}^{mathsf f}(R)$\u0000 , which contains only small objects if and only if R is regular. Recent results of Pollitz, completing work initiated by Dwyer–Greenlees–Iyengar, yield an analogous characterization for complete intersections: R is a complete intersection if and only if every object in \u0000$mathsf {D}^{mathsf f}(R)$\u0000 is proxy small. In this paper, we study a return to the world of R-modules, and search for finitely generated R-modules that are not proxy small whenever R is not a complete intersection. We give an algorithm to construct such modules in certain settings, including over equipresented rings and Stanley–Reisner rings.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"246 1","pages":"412 - 429"},"PeriodicalIF":0.8,"publicationDate":"2020-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nmj.2021.7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49501696","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: 9
POWERS OF BINOMIAL EDGE IDEALS WITH QUADRATIC GRÖBNER BASES 具有二次GRÖBNER基的二项边理想的幂
IF 0.8 2区 数学
Nagoya Mathematical Journal Pub Date : 2020-09-17 DOI: 10.1017/nmj.2021.1
V. Ene, G. Rinaldo, N. Terai
{"title":"POWERS OF BINOMIAL EDGE IDEALS WITH QUADRATIC GRÖBNER BASES","authors":"V. Ene, G. Rinaldo, N. Terai","doi":"10.1017/nmj.2021.1","DOIUrl":"https://doi.org/10.1017/nmj.2021.1","url":null,"abstract":"Abstract We study powers of binomial edge ideals associated with closed and block graphs.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"246 1","pages":"233 - 255"},"PeriodicalIF":0.8,"publicationDate":"2020-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nmj.2021.1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48209106","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: 13
EXACT SOLUTIONS FOR THE SINGULARLY PERTURBED RICCATI EQUATION AND EXACT WKB ANALYSIS 奇异摄动riccati方程的精确解和精确WKB分析
IF 0.8 2区 数学
Nagoya Mathematical Journal Pub Date : 2020-08-14 DOI: 10.1017/nmj.2022.38
Nikita Nikolaev
{"title":"EXACT SOLUTIONS FOR THE SINGULARLY PERTURBED RICCATI EQUATION AND EXACT WKB ANALYSIS","authors":"Nikita Nikolaev","doi":"10.1017/nmj.2022.38","DOIUrl":"https://doi.org/10.1017/nmj.2022.38","url":null,"abstract":"Abstract The singularly perturbed Riccati equation is the first-order nonlinear ordinary differential equation \u0000$hbar partial _x f = af^2 + bf + c$\u0000 in the complex domain where \u0000$hbar $\u0000 is a small complex parameter. We prove an existence and uniqueness theorem for exact solutions with prescribed asymptotics as \u0000$hbar to 0$\u0000 in a half-plane. These exact solutions are constructed using the Borel–Laplace method; that is, they are Borel summations of the formal divergent \u0000$hbar $\u0000 -power series solutions. As an application, we prove existence and uniqueness of exact WKB solutions for the complex one-dimensional Schrödinger equation with a rational potential.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"250 1","pages":"434 - 469"},"PeriodicalIF":0.8,"publicationDate":"2020-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46420925","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: 11
ANALYTIC PROPERTIES OF EISENSTEIN SERIES AND STANDARD $L$-FUNCTIONS EISENSTEIN级数和标准$L$-函数的解析性质
IF 0.8 2区 数学
Nagoya Mathematical Journal Pub Date : 2020-07-21 DOI: 10.1017/nmj.2020.11
O. Stein
{"title":"ANALYTIC PROPERTIES OF EISENSTEIN SERIES AND STANDARD $L$-FUNCTIONS","authors":"O. Stein","doi":"10.1017/nmj.2020.11","DOIUrl":"https://doi.org/10.1017/nmj.2020.11","url":null,"abstract":"We prove a functional equation for a vector valued real analytic Eisenstein series transforming with the Weil representation of $operatorname{Sp}(n,mathbb{Z})$ on $mathbb{C}[(L^{prime }/L)^{n}]$. By relating such an Eisenstein series with a real analytic Jacobi Eisenstein series of degree $n$, a functional equation for such an Eisenstein series is proved. Employing a doubling method for Jacobi forms of higher degree established by Arakawa, we transfer the aforementioned functional equation to a zeta function defined by the eigenvalues of a Jacobi eigenform. Finally, we obtain the analytic continuation and a functional equation of the standard $L$-function attached to a Jacobi eigenform, which was already proved by Murase, however in a different way.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"244 1","pages":"168 - 203"},"PeriodicalIF":0.8,"publicationDate":"2020-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nmj.2020.11","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46414688","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
MAHLER’S AND KOKSMA’S CLASSIFICATIONS IN FIELDS OF POWER SERIES 幂级数域中的MAHLER和KOKSMA分类
IF 0.8 2区 数学
Nagoya Mathematical Journal Pub Date : 2020-07-21 DOI: 10.1017/nmj.2021.5
J. Bell, Y. Bugeaud
{"title":"MAHLER’S AND KOKSMA’S CLASSIFICATIONS IN FIELDS OF POWER SERIES","authors":"J. Bell, Y. Bugeaud","doi":"10.1017/nmj.2021.5","DOIUrl":"https://doi.org/10.1017/nmj.2021.5","url":null,"abstract":"Abstract Let q a prime power and \u0000${mathbb F}_q$\u0000 the finite field of q elements. We study the analogues of Mahler’s and Koksma’s classifications of complex numbers for power series in \u0000${mathbb F}_q((T^{-1}))$\u0000 . Among other results, we establish that both classifications coincide, thereby answering a question of Ooto.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"246 1","pages":"355 - 371"},"PeriodicalIF":0.8,"publicationDate":"2020-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nmj.2021.5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43579128","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
NMJ volume 238 Cover and Back matter NMJ卷238封面和封底
IF 0.8 2区 数学
Nagoya Mathematical Journal Pub Date : 2020-06-01 DOI: 10.1017/s0027763020000057
{"title":"NMJ volume 238 Cover and Back matter","authors":"","doi":"10.1017/s0027763020000057","DOIUrl":"https://doi.org/10.1017/s0027763020000057","url":null,"abstract":"","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"238 1","pages":"b1 - b2"},"PeriodicalIF":0.8,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/s0027763020000057","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45708175","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
NMJ volume 238 Cover and Front matter NMJ卷238封面和正面问题
IF 0.8 2区 数学
Nagoya Mathematical Journal Pub Date : 2020-06-01 DOI: 10.1017/s0027763020000045
{"title":"NMJ volume 238 Cover and Front matter","authors":"","doi":"10.1017/s0027763020000045","DOIUrl":"https://doi.org/10.1017/s0027763020000045","url":null,"abstract":"","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"238 1","pages":"f1 - f4"},"PeriodicalIF":0.8,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/s0027763020000045","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45638729","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
NORMAL AND IRREDUCIBLE ADIC SPACES, THE OPENNESS OF FINITE MORPHISMS, AND A STEIN FACTORIZATION 正规和不可约ADIC空间、有限态射的开放性和STEIN因子分解
IF 0.8 2区 数学
Nagoya Mathematical Journal Pub Date : 2020-05-14 DOI: 10.1017/nmj.2022.40
L. Mann
{"title":"NORMAL AND IRREDUCIBLE ADIC SPACES, THE OPENNESS OF FINITE MORPHISMS, AND A STEIN FACTORIZATION","authors":"L. Mann","doi":"10.1017/nmj.2022.40","DOIUrl":"https://doi.org/10.1017/nmj.2022.40","url":null,"abstract":"Abstract We transfer several elementary geometric properties of rigid-analytic spaces to the world of adic spaces, more precisely to the category of adic spaces which are locally of (weakly) finite type over a non-archimedean field. This includes normality, irreducibility (in particular, irreducible components), and a Stein factorization theorem. Most notably, we show that a finite morphism in our category of adic spaces is automatically open if the target is normal and both source and target are of the same pure dimension. Moreover, our version of the Stein factorization theorem includes a statement about the geometric connectedness of fibers which we have not found in the literature of rigid-analytic or Berkovich spaces.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"250 1","pages":"498 - 510"},"PeriodicalIF":0.8,"publicationDate":"2020-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41997889","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: 4
ON THE HEIGHT AND RELATIONAL COMPLEXITY OF A FINITE PERMUTATION GROUP 有限置换群的高度与关系复杂度
IF 0.8 2区 数学
Nagoya Mathematical Journal Pub Date : 2020-05-08 DOI: 10.1017/nmj.2021.6
Nick Gill, Bianca Lod'a, Pablo Spiga
{"title":"ON THE HEIGHT AND RELATIONAL COMPLEXITY OF A FINITE PERMUTATION GROUP","authors":"Nick Gill, Bianca Lod'a, Pablo Spiga","doi":"10.1017/nmj.2021.6","DOIUrl":"https://doi.org/10.1017/nmj.2021.6","url":null,"abstract":"Abstract Let G be a permutation group on a set \u0000$Omega $\u0000 of size t. We say that \u0000$Lambda subseteq Omega $\u0000 is an independent set if its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset of \u0000$Lambda $\u0000 . We define the height of G to be the maximum size of an independent set, and we denote this quantity \u0000$textrm{H}(G)$\u0000 . In this paper, we study \u0000$textrm{H}(G)$\u0000 for the case when G is primitive. Our main result asserts that either \u0000$textrm{H}(G)< 9log t$\u0000 or else G is in a particular well-studied family (the primitive large–base groups). An immediate corollary of this result is a characterization of primitive permutation groups with large relational complexity, the latter quantity being a statistic introduced by Cherlin in his study of the model theory of permutation groups. We also study \u0000$textrm{I}(G)$\u0000 , the maximum length of an irredundant base of G, in which case we prove that if G is primitive, then either \u0000$textrm{I}(G)<7log t$\u0000 or else, again, G is in a particular family (which includes the primitive large–base groups as well as some others).","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"246 1","pages":"372 - 411"},"PeriodicalIF":0.8,"publicationDate":"2020-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nmj.2021.6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42366286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
ON THE DEPTH OF SYMBOLIC POWERS OF EDGE IDEALS OF GRAPHS 论图的边理想的符号幂的深度
IF 0.8 2区 数学
Nagoya Mathematical Journal Pub Date : 2020-04-10 DOI: 10.1017/nmj.2020.27
S. Fakhari
{"title":"ON THE DEPTH OF SYMBOLIC POWERS OF EDGE IDEALS OF GRAPHS","authors":"S. Fakhari","doi":"10.1017/nmj.2020.27","DOIUrl":"https://doi.org/10.1017/nmj.2020.27","url":null,"abstract":"Abstract Assume that G is a graph with edge ideal \u0000$I(G)$\u0000 and star packing number \u0000$alpha _2(G)$\u0000 . We denote the sth symbolic power of \u0000$I(G)$\u0000 by \u0000$I(G)^{(s)}$\u0000 . It is shown that the inequality \u0000$ operatorname {mathrm {depth}} S/(I(G)^{(s)})geq alpha _2(G)-s+1$\u0000 is true for every chordal graph G and every integer \u0000$sgeq 1$\u0000 . Moreover, it is proved that for any graph G, we have \u0000$ operatorname {mathrm {depth}} S/(I(G)^{(2)})geq alpha _2(G)-1$\u0000 .","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"245 1","pages":"28 - 40"},"PeriodicalIF":0.8,"publicationDate":"2020-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nmj.2020.27","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45656808","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: 5
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