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Bounding projective hypersurface singularities 限定投影超曲面奇点
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2024-10-15 DOI: 10.1016/j.aim.2024.109970
Ben Castor
{"title":"Bounding projective hypersurface singularities","authors":"Ben Castor","doi":"10.1016/j.aim.2024.109970","DOIUrl":"10.1016/j.aim.2024.109970","url":null,"abstract":"<div><div>We compare several different methods involving Hodge-theoretic spectra of singularities which produce constraints on the number and type of isolated singularities on a projective hypersurface of fixed degree. In particular, we introduce a method based on the spectrum of the nonisolated singularity at the origin of the affine cone on such a hypersurface, and relate the resulting explicit formula to Varchenko's bound.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Higher Chow groups with finite coefficients and refined unramified cohomology 具有有限系数的高等周群与精制无ramified同调
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2024-10-15 DOI: 10.1016/j.aim.2024.109972
Kees Kok , Lin Zhou
{"title":"Higher Chow groups with finite coefficients and refined unramified cohomology","authors":"Kees Kok ,&nbsp;Lin Zhou","doi":"10.1016/j.aim.2024.109972","DOIUrl":"10.1016/j.aim.2024.109972","url":null,"abstract":"<div><div>In this paper we show that Bloch's higher cycle class map with finite coefficients for quasi-projective equi-dimensional schemes over a field fits naturally in a long exact sequence involving Schreieder's refined unramified cohomology. We also show that the refined unramified cohomology satisfies the localization sequence. Using this we conjecture in the end that refined unramified cohomology is a motivic homology theory and explain how this is related to the aforementioned results.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Blow-up invariance of cohomology theories with modulus 有模同调理论的胀大不变性
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2024-10-14 DOI: 10.1016/j.aim.2024.109967
Junnosuke Koizumi
{"title":"Blow-up invariance of cohomology theories with modulus","authors":"Junnosuke Koizumi","doi":"10.1016/j.aim.2024.109967","DOIUrl":"10.1016/j.aim.2024.109967","url":null,"abstract":"<div><div>In this paper, we study cohomology theories of <span><math><mi>Q</mi></math></span>-modulus pairs, which are pairs <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></span> consisting of a scheme <em>X</em> and a <span><math><mi>Q</mi></math></span>-divisor <em>D</em>. Our main theorem provides a sufficient condition for such a cohomology theory to be invariant under blow-ups with centers contained in the divisor. This yields a short proof of the blow-up invariance of the Hodge cohomology with modulus proved by Kelly-Miyazaki. We also define the Witt vector cohomology with modulus using the Brylinski-Kato filtration and prove its blow-up invariance.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 a method of Hurwitz and its applications 论赫尔维茨方法及其应用
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2024-10-11 DOI: 10.1016/j.aim.2024.109968
W. Duke , Ö. Imamoḡlu , Á. Tóth
{"title":"On a method of Hurwitz and its applications","authors":"W. Duke ,&nbsp;Ö. Imamoḡlu ,&nbsp;Á. Tóth","doi":"10.1016/j.aim.2024.109968","DOIUrl":"10.1016/j.aim.2024.109968","url":null,"abstract":"<div><div>We give class number formulas for binary cubic and <em>n</em>-ary quadratic forms using a method of Hurwitz. We also show how the same method can be applied to give identities for certain multiple zeta values attached to symmetric cones.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142424644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
The C-motivic Adams-Novikov spectral sequence for topological modular forms 拓扑模块形式的 C 动力亚当斯-诺维科夫谱序列
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2024-10-08 DOI: 10.1016/j.aim.2024.109966
Daniel C. Isaksen , Hana Jia Kong , Guchuan Li , Yangyang Ruan , Heyi Zhu
{"title":"The C-motivic Adams-Novikov spectral sequence for topological modular forms","authors":"Daniel C. Isaksen ,&nbsp;Hana Jia Kong ,&nbsp;Guchuan Li ,&nbsp;Yangyang Ruan ,&nbsp;Heyi Zhu","doi":"10.1016/j.aim.2024.109966","DOIUrl":"10.1016/j.aim.2024.109966","url":null,"abstract":"<div><div>We analyze the <span><math><mi>C</mi></math></span>-motivic (and classical) Adams-Novikov spectral sequence for the <span><math><mi>C</mi></math></span>-motivic modular forms spectrum <em>mmf</em> (and for the classical topological modular forms spectrum <em>tmf</em>). We primarily use purely algebraic techniques, with a few exceptions. Along the way, we settle a previously unresolved detail about the multiplicative structure of the homotopy groups of <em>tmf</em>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142424643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Non-algebraic geometrically trivial cohomology classes over finite fields 有限域上的非代数几何琐碎同调类
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2024-10-07 DOI: 10.1016/j.aim.2024.109964
Federico Scavia , Fumiaki Suzuki
{"title":"Non-algebraic geometrically trivial cohomology classes over finite fields","authors":"Federico Scavia ,&nbsp;Fumiaki Suzuki","doi":"10.1016/j.aim.2024.109964","DOIUrl":"10.1016/j.aim.2024.109964","url":null,"abstract":"<div><div>We give the first examples of smooth projective varieties <em>X</em> over a finite field <span><math><mi>F</mi></math></span> admitting a non-algebraic torsion <em>ℓ</em>-adic cohomology class of degree 4 which vanishes over <span><math><mover><mrow><mi>F</mi></mrow><mo>‾</mo></mover></math></span>. We use them to show that two versions of the integral Tate conjecture over <span><math><mi>F</mi></math></span> are not equivalent to one another and that a fundamental exact sequence of Colliot-Thélène and Kahn does not necessarily split. Some of our examples have dimension 4, and are the first known examples of fourfolds with non-vanishing <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mi>nr</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mo>(</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>/</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mn>2</mn><mo>)</mo><mo>)</mo></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Zeta functions for spherical tits buildings of finite general linear groups 有限一般线性群球形山雀建筑的 Zeta 函数
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2024-10-04 DOI: 10.1016/j.aim.2024.109965
Jianhao Shen
{"title":"Zeta functions for spherical tits buildings of finite general linear groups","authors":"Jianhao Shen","doi":"10.1016/j.aim.2024.109965","DOIUrl":"10.1016/j.aim.2024.109965","url":null,"abstract":"<div><div>In this paper, we define edge zeta functions for spherical buildings associated with finite general linear groups. We derive elegant formulas for these zeta functions and reveal patterns of eigenvalues of these buildings, by introducing and applying insightful tools including digraphs <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, cyclic <em>n</em>-partite graphs, partite-transitive group actions, and Springer's theorem on Hecke algebras.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
The category of topological spaces and open maps does not have products 拓扑空间和开放映射范畴没有乘积
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2024-10-03 DOI: 10.1016/j.aim.2024.109963
Guram Bezhanishvili , Andre Kornell
{"title":"The category of topological spaces and open maps does not have products","authors":"Guram Bezhanishvili ,&nbsp;Andre Kornell","doi":"10.1016/j.aim.2024.109963","DOIUrl":"10.1016/j.aim.2024.109963","url":null,"abstract":"<div><div>We prove that the category of topological spaces and open maps does not have binary products, thus resolving the Esakia problem in the negative. We also prove that the category of Kripke frames does not have binary products and that the category of complete Heyting algebras does not have binary coproducts.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
From local nets to Euler elements 从局部网到欧拉元素
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2024-10-01 DOI: 10.1016/j.aim.2024.109960
Vincenzo Morinelli, Karl-Hermann Neeb
{"title":"From local nets to Euler elements","authors":"Vincenzo Morinelli,&nbsp;Karl-Hermann Neeb","doi":"10.1016/j.aim.2024.109960","DOIUrl":"10.1016/j.aim.2024.109960","url":null,"abstract":"<div><div>Various aspects of the geometric setting of Algebraic Quantum Field Theory (AQFT) models related to representations of the Poincaré group can be studied for general Lie groups, whose Lie algebra contains an Euler element, i.e., ad <em>h</em> is diagonalizable with eigenvalues in <span><math><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></span>. This has been explored by the authors and their collaborators during recent years. A key property in this construction is the Bisognano–Wichmann property (thermal property for wedge region algebras) concerning the geometric implementation of modular groups of local algebras.</div><div>In the present paper we prove that under a natural regularity condition, geometrically implemented modular groups arising from the Bisognano–Wichmann property are always generated by Euler elements. We also show the converse, namely that in presence of Euler elements and the Bisognano–Wichmann property, regularity and localizability hold in a quite general setting. Lastly we show that, in this generalized AQFT, in the vacuum representation, under analogous assumptions (regularity and Bisognano–Wichmann), the von Neumann algebras associated to wedge regions are type III<sub>1</sub> factors, a property that is well-known in the AQFT context.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
A motivic pairing and the Mellin transform in function fields 函数场中的动机配对和梅林变换
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2024-10-01 DOI: 10.1016/j.aim.2024.109962
Nathan Green
{"title":"A motivic pairing and the Mellin transform in function fields","authors":"Nathan Green","doi":"10.1016/j.aim.2024.109962","DOIUrl":"10.1016/j.aim.2024.109962","url":null,"abstract":"<div><div>We define two pairings relating the <em>A</em>-motive with the dual <em>A</em>-motive of an abelian Anderson <em>A</em>-module. We show that specializations of these pairings give the exponential and logarithm functions of this Anderson <em>A</em>-module, and we use these specializations to give precise formulas for the coefficients of the exponential and logarithm functions. We then use these pairings to express the exponential and logarithm functions as evaluations of certain infinite products. As an application of these ideas, we prove an analogue of the Mellin transform formula for the Riemann zeta function in the case of Carlitz zeta values. We also give an example showing how our results apply to Carlitz multiple zeta values.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
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