Journal of Pure and Applied Algebra最新文献

Jacobian varieties with group algebra decomposition not affordable by Prym varieties 具有群代数分解的雅各布品种不是普莱姆品种所能负担得起的

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-09-13 DOI: 10.1016/j.jpaa.2024.107803

{"title":"Jacobian varieties with group algebra decomposition not affordable by Prym varieties","authors":"","doi":"10.1016/j.jpaa.2024.107803","DOIUrl":"10.1016/j.jpaa.2024.107803","url":null,"abstract":"<div><div>The action of a finite group G on a compact Riemann surface X naturally induces another action of G on its Jacobian variety <math><mi>J</mi><mo>(</mo><mi>X</mi><mo>)</mo></math>. In many cases, each component of the group algebra decomposition of <math><mi>J</mi><mo>(</mo><mi>X</mi><mo>)</mo></math> is isogenous to a Prym varieties of an intermediate covering of the Galois covering <math><msub><mrow><mi>π</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>:</mo><mi>X</mi><mo>→</mo><mi>X</mi><mo>/</mo><mi>G</mi></math>; in such a case, we say that the group algebra decomposition is affordable by Prym varieties. In this article, we present an infinite family of groups that act on Riemann surfaces in a manner that the group algebra decomposition of <math><mi>J</mi><mo>(</mo><mi>X</mi><mo>)</mo></math> is not affordable by Prym varieties; namely, affine groups <math><mi>Aff</mi><mo>(</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>)</mo></math> with some exceptions: <math><mi>q</mi><mo>=</mo><mn>2</mn></math>, <math><mi>q</mi><mo>=</mo><mn>9</mn></math>, q a Fermat prime, <math><mi>q</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup></math> with <math><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>−</mo><mn>1</mn></math> a Mersenne prime and some particular cases when <math><mi>X</mi><mo>/</mo><mi>G</mi></math> has genus 0 or 1. In each one of this exceptional cases, we give the group algebra decomposition of <math><mi>J</mi><mo>(</mo><mi>X</mi><mo>)</mo></math> by Prym varieties.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315895","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 transcendental lattices of Hyper-Kähler manifolds 论超凯勒流形的超越网格

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-09-12 DOI: 10.1016/j.jpaa.2024.107805

引用次数: 0

Some remarks on spin-orbits of unit vectors 关于单位矢量自旋轨道的一些评论

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-09-10 DOI: 10.1016/j.jpaa.2024.107802

引用次数: 0

On local divisor class groups of complete intersections 论完全相交的局部除数类群

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-09-10 DOI: 10.1016/j.jpaa.2024.107804

{"title":"On local divisor class groups of complete intersections","authors":"","doi":"10.1016/j.jpaa.2024.107804","DOIUrl":"10.1016/j.jpaa.2024.107804","url":null,"abstract":"<div>Samuel conjectured in 1961 that a (Noetherian) local complete intersection ring that is a UFD in codimension at most three is itself a UFD. It is said that Grothendieck invented local cohomology to prove this fact. Following the philosophy that a UFD is nothing else than a Krull domain (that is, a normal domain, in the Noetherian case) with trivial divisor class group, we take a closer look at the Samuel–Grothendieck Theorem and prove the following generalization: Let A be a local Cohen–Macaulay ring.<ul><li>(1)A is a normal domain if and only if A is a normal domain in codimension at most 1.</li><li>(2)Suppose that A is a normal domain and a complete intersection. Then the divisor class group of A is a subgroup of the projective limit of the divisor class groups of the localizations <math><msub><mrow><mi>A</mi></mrow><mrow><mi>p</mi></mrow></msub></math>, where p runs through all prime ideals of height at most 3 in A.</li></ul> We use this fact to describe for an integral Noetherian locally complete intersection scheme X the gap between the groups of Weil and Cartier divisors, generalizing in this case the classical result that these two concepts coincide if X is locally a UFD.</div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022404924002019/pdfft?md5=1e4c0d69cfcf0e52b73f98c66deb7d97&pid=1-s2.0-S0022404924002019-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142168841","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

Some remarks on relative modular categories 关于相对模块类别的一些评论

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-09-10 DOI: 10.1016/j.jpaa.2024.107801

引用次数: 0

Skew power series rings over a prime base ring 素基环上的斜幂级数环

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-09-10 DOI: 10.1016/j.jpaa.2024.107800

{"title":"Skew power series rings over a prime base ring","authors":"","doi":"10.1016/j.jpaa.2024.107800","DOIUrl":"10.1016/j.jpaa.2024.107800","url":null,"abstract":"<div>In this paper, we investigate the structure of skew power series rings of the form <math><mi>S</mi><mo>=</mo><mi>R</mi><mo>[</mo><mo>[</mo><mi>x</mi><mo>;</mo><mi>σ</mi><mo>,</mo><mi>δ</mi><mo>]</mo><mo>]</mo></math>, where R is a complete, positively filtered ring and <math><mo>(</mo><mi>σ</mi><mo>,</mo><mi>δ</mi><mo>)</mo></math> is a skew derivation respecting the filtration. Our main focus is on the case in which <math><mi>σ</mi><mi>δ</mi><mo>=</mo><mi>δ</mi><mi>σ</mi></math>, and we aim to use techniques in non-commutative valuation theory to address the long-standing open question: if P is an invariant prime ideal of R, is PS a prime ideal of S? When R has characteristic p, our results reduce this to a finite-index problem. We also give preliminary results in the “Iwasawa algebra” case <math><mi>δ</mi><mo>=</mo><mi>σ</mi><mo>−</mo><msub><mrow><mi>id</mi></mrow><mrow><mi>R</mi></mrow></msub></math> in arbitrary characteristic. A key step in our argument will be to show that for a large class of Noetherian algebras, the nilradical is “almost” <math><mo>(</mo><mi>σ</mi><mo>,</mo><mi>δ</mi><mo>)</mo></math>-invariant in a certain sense.</div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002240492400197X/pdfft?md5=13b400d1c28154510e7fe3158aa43840&pid=1-s2.0-S002240492400197X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142237327","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

Characteristic p approaches to the Jacobian conjecture 雅各布猜想的特征 p 方法

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-09-07 DOI: 10.1016/j.jpaa.2024.107797

引用次数: 0

Classifying torsionfree classes of the category of coherent sheaves and their Serre subcategories 相干剪切范畴的无扭类及其塞尔子范畴的分类

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-09-05 DOI: 10.1016/j.jpaa.2024.107799

引用次数: 0

On the Drinfeld double of the restricted Jordan plane in characteristic 2 论特征 2 中受限约旦平面的德林费尔德双倍性

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-09-05 DOI: 10.1016/j.jpaa.2024.107798

引用次数: 0

The classification of automorphisms and quotients of Calabi-Yau threefolds of type A A 型 Calabi-Yau 三折的自形和商的分类

IF 0.7 2区数学

Journal of Pure and Applied Algebra Pub Date : 2024-08-30 DOI: 10.1016/j.jpaa.2024.107796

{"title":"The classification of automorphisms and quotients of Calabi-Yau threefolds of type A","authors":"","doi":"10.1016/j.jpaa.2024.107796","DOIUrl":"10.1016/j.jpaa.2024.107796","url":null,"abstract":"<div>The aim of the paper is to investigate the only two families <math><msubsup><mrow><mi>F</mi></mrow><mrow><mi>G</mi></mrow><mrow><mi>A</mi></mrow></msubsup></math> of Calabi-Yau 3-folds <math><mi>A</mi><mo>/</mo><mi>G</mi></math> with A an abelian 3-fold and <math><mi>G</mi><mo>≤</mo><mtext>Aut</mtext><mo>(</mo><mi>A</mi><mo>)</mo></math> a finite group acting freely: one is constructed in [11] and the other is presented here. We provide a complete classification of the automorphism group of <math><mi>X</mi><mo>∈</mo><msubsup><mrow><mi>F</mi></mrow><mrow><mi>G</mi></mrow><mrow><mi>A</mi></mrow></msubsup></math>. Additionally, we construct and classify the quotients <math><mi>X</mi><mo>/</mo><mi>ϒ</mi></math> for any <math><mi>ϒ</mi><mo>≤</mo><mtext>Aut</mtext><mo>(</mo><mi>X</mi><mo>)</mo></math>. Specifically, for those groups ϒ that preserve the volume form of X then <math><mi>X</mi><mo>/</mo><mi>ϒ</mi></math> admits a desingularization Y which is a Calabi-Yau 3-fold: we compute the Hodge numbers and the fundamental group of these Y, thereby determining all topological in-equivalent Calabi-Yau 3-folds obtained in this way.</div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223258","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