Journal of the London Mathematical Society-Second Series最新文献

Geometry of Selberg's bisectors in the symmetric space S L ( n , R ) / S O ( n , R ) $SL(n,mathbb {R})/SO(n,mathbb {R})$ 对称空间 S L ( n , R ) / S O ( n , R ) 中塞尔伯格平分线的几何学 $SL(n,mathbb {R})/SO(n,mathbb {R})$

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-26 DOI: 10.1112/jlms.12992

Yukun Du

{"title":"Geometry of Selberg's bisectors in the symmetric space \u0000 \u0000 \u0000 S\u0000 L\u0000 (\u0000 n\u0000 ,\u0000 R\u0000 )\u0000 /\u0000 S\u0000 O\u0000 (\u0000 n\u0000 ,\u0000 R\u0000 )\u0000 \u0000 $SL(n,mathbb {R})/SO(n,mathbb {R})$","authors":"Yukun Du","doi":"10.1112/jlms.12992","DOIUrl":"https://doi.org/10.1112/jlms.12992","url":null,"abstract":"I study several problems about the symmetric space associated with the Lie group <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$SL(n,mathbb {R})$</annotation>\u0000 </semantics></math>. These problems are connected to an algorithm based on Poincaré's Fundamental Polyhedron Theorem, designed to determine generalized geometric finiteness properties for subgroups of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$SL(n,mathbb {R})$</annotation>\u0000 </semantics></math>. The algorithm is analogous to the original one in hyperbolic spaces, while the Riemannian distance is replaced by an <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$SL(n,mathbb {R})$</annotation>\u0000 </semantics></math>-invariant premetric. The main results of this paper are twofold. In the first part, I focus on questions that occurred in generalizing Poincaré's Algorithm to my symmetric space. I describe and implement an algorithm that computes the face-poset structure of finitely sided polyhedra, and construct an angle-like function between hyperplanes. In the second part, I study further questions related to hyperplanes and Dirichlet–Selberg domains in my symmetric space. I establish several criteria for the disjointness of hyperplanes and classify particular Abelian subgroups of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <mn>3</mn>\u0000 <mo>,</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$SL(3,mathbb {R})$</annotation>\u0000 </semantics></math> based on whether their Dirichlet–Selberg domains are finitely sided or not.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142324526","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 tame ramification and centers of F $F$ -purity 论 F $F$ 纯度的驯服斜面和中心

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-26 DOI: 10.1112/jlms.12993

Javier Carvajal-Rojas, Anne Fayolle

{"title":"On tame ramification and centers of \u0000 \u0000 F\u0000 $F$\u0000 -purity","authors":"Javier Carvajal-Rojas, Anne Fayolle","doi":"10.1112/jlms.12993","DOIUrl":"https://doi.org/10.1112/jlms.12993","url":null,"abstract":"We introduce a notion of tame ramification for general finite covers. When specialized to the separable case, it extends to higher dimensions the classical notion of tame ramification for Dedekind domains and curves and sits nicely in between other notions of tame ramification in arithmetic geometry. However, when applied to the Frobenius map, it naturally yields the notion of center of <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-purity (aka compatibly <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-split subvariety). As an application, we describe the behavior of centers of <math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-purity under finite covers — it all comes down to a transitivity property for tame ramification in towers.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12993","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142324524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Asymmetric distribution of extreme values of cubic L $L$ -functions at s = 1 $s=1$ 立方 L $L$ 函数极值在 s = 1 $s=1$ 时的非对称分布

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-24 DOI: 10.1112/jlms.12996

Pranendu Darbar, Chantal David, Matilde Lalin, Allysa Lumley

{"title":"Asymmetric distribution of extreme values of cubic \u0000 \u0000 L\u0000 $L$\u0000 -functions at \u0000 \u0000 \u0000 s\u0000 =\u0000 1\u0000 \u0000 $s=1$","authors":"Pranendu Darbar, Chantal David, Matilde Lalin, Allysa Lumley","doi":"10.1112/jlms.12996","DOIUrl":"https://doi.org/10.1112/jlms.12996","url":null,"abstract":"We investigate the distribution of values of cubic Dirichlet <math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>-functions at <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$s=1$</annotation>\u0000 </semantics></math>. Following ideas of Granville and Soundararajan for quadratic <math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>-functions, we model the distribution of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>χ</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$L(1,chi)$</annotation>\u0000 </semantics></math> by the distribution of random Euler products <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>X</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$L(1,mathbb {X})$</annotation>\u0000 </semantics></math> for certain family of random variables <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathbb {X}(p)$</annotation>\u0000 </semantics></math> attached to each prime. We obtain a description of the proportion of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>χ</mi>\u0000 <mo>)</mo>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <annotation>$|L(1,chi)|$</annotation>\u0000 </semantics></math> that is larger or that is smaller than a given bound, and yield more light into the Littlewood bounds. Unlike the quadratic case, there is an asymmetry between lower and upper bounds for the cubic case, and small values are less probable than large values.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12996","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142320667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rational points on complete intersections of cubic and quadric hypersurfaces over F q ( t ) $mathbb {F}_q(t)$ F q ( t ) $mathbb {F}_q(t)$ 上三次方和二次方超曲面完全交点上的有理点

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-24 DOI: 10.1112/jlms.12991

Jakob Glas

{"title":"Rational points on complete intersections of cubic and quadric hypersurfaces over \u0000 \u0000 \u0000 \u0000 F\u0000 q\u0000 \u0000 \u0000 (\u0000 t\u0000 )\u0000 \u0000 \u0000 $mathbb {F}_q(t)$","authors":"Jakob Glas","doi":"10.1112/jlms.12991","DOIUrl":"https://doi.org/10.1112/jlms.12991","url":null,"abstract":"Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>q</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathbb {F}_q(t)$</annotation>\u0000 </semantics></math>, provided <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>char</mo>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>q</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 <mo>></mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$operatorname{char}(mathbb {F}_q)&gt;3$</annotation>\u0000 </semantics></math>. Under the same hypotheses, we also verify weak approximation.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12991","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142320668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Varieties over Q ¯ $overline{mathbb {Q}}$ with infinite Chow groups modulo almost all primes 在几乎所有素数上具有无限周群的 Q ¯$overline{mathbb {Q}}$ 上的变项

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-20 DOI: 10.1112/jlms.12994

Federico Scavia

{"title":"Varieties over \u0000 \u0000 \u0000 Q\u0000 ¯\u0000 \u0000 $overline{mathbb {Q}}$\u0000 with infinite Chow groups modulo almost all primes","authors":"Federico Scavia","doi":"10.1112/jlms.12994","DOIUrl":"https://doi.org/10.1112/jlms.12994","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$E$</annotation>\u0000 </semantics></math> be the Fermat cubic curve over <math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>Q</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <annotation>$overline{mathbb {Q}}$</annotation>\u0000 </semantics></math>. In 2002, Schoen proved that the group <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>E</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>/</mo>\u0000 <mi>ℓ</mi>\u0000 </mrow>\u0000 <annotation>$CH^2(E^3)/ell$</annotation>\u0000 </semantics></math> is infinite for all primes <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 <mo>≡</mo>\u0000 <mn>1</mn>\u0000 <mspace></mspace>\u0000 <mo>(</mo>\u0000 <mi>mod</mi>\u0000 <mspace></mspace>\u0000 <mn>3</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$ell equiv 1pmod 3$</annotation>\u0000 </semantics></math>. We show that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>E</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>/</mo>\u0000 <mi>ℓ</mi>\u0000 </mrow>\u0000 <annotation>$CH^2(E^3)/ell$</annotation>\u0000 </semantics></math> is infinite for all prime numbers <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 <mo>></mo>\u0000 <mn>5</mn>\u0000 </mrow>\u0000 <annotation>$ell &gt; 5$</annotation>\u0000 </semantics></math>. This gives the first example of a smooth projective variety <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$X$</annotation>\u0000 </semantics></math> over <math>\u0000 <semantics>\u0000 <mover>\u0000 <mi>Q</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <annotation>$overline{mathbb {Q}}$</annotation>\u0000 </semantics></math> such that <math>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142273162","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

Countably tight dual ball with a nonseparable measure 具有不可分割度量的可数紧密对偶球

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-20 DOI: 10.1112/jlms.12988

Piotr Koszmider, Zdeněk Silber

{"title":"Countably tight dual ball with a nonseparable measure","authors":"Piotr Koszmider, Zdeněk Silber","doi":"10.1112/jlms.12988","DOIUrl":"https://doi.org/10.1112/jlms.12988","url":null,"abstract":"We construct a compact Hausdorff space <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> such that the space <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 <mo>(</mo>\u0000 <mi>K</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$P(K)$</annotation>\u0000 </semantics></math> of Radon probability measures on <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> considered with the <math>\u0000 <semantics>\u0000 <msup>\u0000 <mtext>weak</mtext>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$text{weak}^*$</annotation>\u0000 </semantics></math> topology (induced from the space of continuous functions <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 <mo>(</mo>\u0000 <mi>K</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$C(K)$</annotation>\u0000 </semantics></math>) is countably tight that is a generalization of sequentiality (i.e., if a measure <math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math> is in the closure of a set <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>, there is a countable <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>M</mi>\u0000 <mo>′</mo>\u0000 </msup>\u0000 <mo>⊆</mo>\u0000 <mi>M</mi>\u0000 </mrow>\u0000 <annotation>$M^{prime }subseteq M$</annotation>\u0000 </semantics></math> such that <math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math> is in the closure of <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>M</mi>\u0000 <mo>′</mo>\u0000 </msup>\u0000 <annotation>$M^{prime }$</annotation>\u0000 </semantics></math>) but <math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> carries a Radon probability measure that has uncountable Maharam type (i.e., <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>μ</mi>\u0000 <mo>)</mo>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142273161","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

Effective generic freeness and applications to local cohomology 有效通用自由性及其在局部同调中的应用

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-20 DOI: 10.1112/jlms.12995

Yairon Cid-Ruiz, Ilya Smirnov

{"title":"Effective generic freeness and applications to local cohomology","authors":"Yairon Cid-Ruiz, Ilya Smirnov","doi":"10.1112/jlms.12995","DOIUrl":"https://doi.org/10.1112/jlms.12995","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> be a Noetherian domain and <math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math> be a finitely generated <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>-algebra. We study several features regarding the generic freeness over <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> of an <math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math>-module. For an ideal <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>I</mi>\u0000 <mo>⊂</mo>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$I subset R$</annotation>\u0000 </semantics></math>, we show that the local cohomology modules <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>H</mi>\u0000 <mi>I</mi>\u0000 <mi>i</mi>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$normalfont text{H}_I^i(R)$</annotation>\u0000 </semantics></math> are generically free over <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> under certain settings where <math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math> is a smooth <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math>-algebra. By utilizing the theory of Gröbner bases over arbitrary Noetherian rings, we provide an effective method to b make explicit the generic freeness over <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$A$</annotation>\u0000 </semantics></math> of a finitely generated <math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$R$</annotation>\u0000 </semantics></math>-module.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142273278","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

Time-periodic solutions to heated ferrofluid flow models 加热铁流体流动模型的时周期解法

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-18 DOI: 10.1112/jlms.12990

Kamel Hamdache, Djamila Hamroun, Basma Jaffal-Mourtada

引用次数: 0

Fullness of q $q$ -Araki-Woods factors qq$ 的饱满度 -阿拉基-伍兹系数

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-18 DOI: 10.1112/jlms.12989

Manish Kumar, Simeng Wang

引用次数: 0

Lattice reduced and complete convex bodies 晶格缩小和完整凸体

IF 1 2区数学

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-17 DOI: 10.1112/jlms.12982

Giulia Codenotti, Ansgar Freyer

{"title":"Lattice reduced and complete convex bodies","authors":"Giulia Codenotti, Ansgar Freyer","doi":"10.1112/jlms.12982","DOIUrl":"https://doi.org/10.1112/jlms.12982","url":null,"abstract":"The purpose of this paper is to study convex bodies <math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$C$</annotation>\u0000 </semantics></math> for which there exists no convex body <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>′</mo>\u0000 </msup>\u0000 <mi>⊊</mi>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <annotation>$C^prime subsetneq C$</annotation>\u0000 </semantics></math> of the same lattice width. Such bodies will be called ‘lattice reduced’, and they occur naturally in the study of the flatness constant in integer programming, as well as other problems related to lattice width. We show that any simplex that realizes the flatness constant must be lattice reduced and prove structural properties of general lattice reduced convex bodies: they are polytopes with at most <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mn>2</mn>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$2^{d+1}-2$</annotation>\u0000 </semantics></math> vertices and their lattice width is attained by at least <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>(</mo>\u0000 <mi>log</mi>\u0000 <mi>d</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Omega (log d)$</annotation>\u0000 </semantics></math> independent directions. Strongly related to lattice reduced bodies are the ‘lattice complete bodies’, which are convex bodies <math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$C$</annotation>\u0000 </semantics></math> for which there exists no <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>′</mo>\u0000 </msup>\u0000 <mo>⊋</mo>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <annotation>$C^prime supsetneq C$</annotation>\u0000 </semantics></math> such that <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>′</mo>\u0000 </msup>\u0000 <annotation>$C^prime$</annotation>\u0000 </semantics></math> has the same lattice diameter as <math>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12982","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142244976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0