Indagationes Mathematicae-New Series最新文献_第6页

Global Galois symbols on E×E 全球伽罗瓦符号在E×E

IF 0.8 4区数学

Indagationes Mathematicae-New Series Pub Date : 2026-01-01 Epub Date: 2024-11-16 DOI: 10.1016/j.indag.2024.11.004

Dinakar Ramakrishnan

{"title":"Global Galois symbols on E×E","authors":"Dinakar Ramakrishnan","doi":"10.1016/j.indag.2024.11.004","DOIUrl":"10.1016/j.indag.2024.11.004","url":null,"abstract":"<div><div>Let <math><mi>E</mi></math> be an elliptic curve over a number field <math><mi>F</mi></math>, <math><mi>A</mi></math> the abelian surface <math><mrow><mi>E</mi><mo>×</mo><mi>E</mi></mrow></math>, and <math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>F</mi></mrow></msub><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow></mrow></math> the F-rational albanese kernel of <math><mi>A</mi></math>, which is a subgroup of the degree zero part of Chow group of zero cycles on <math><mi>A</mi></math> modulo rational equivalence. The first result is that for all but a finite number of primes <math><mi>p</mi></math> where <math><mi>E</mi></math> has ordinary reduction, the image of <math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>F</mi></mrow></msub><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mo>/</mo><mi>p</mi></mrow></math> in the Galois cohomology group <math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>F</mi><mo>,</mo><msup><mrow><mi>sym</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>E</mi><mrow><mo>[</mo><mi>p</mi><mo>]</mo></mrow><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math> is zero; here <math><mrow><mi>E</mi><mrow><mo>[</mo><mi>p</mi><mo>]</mo></mrow></mrow></math> denotes as usual the Galois module of p-division points on <math><mi>E</mi></math>. The second result is that for any prime <math><mi>p</mi></math> where <math><mi>E</mi></math> has good ordinary reduction, there is a finite extension <math><mi>K</mi></math> of <math><mi>F</mi></math>, depending on <math><mi>p</mi></math> and <math><mi>E</mi></math>, such that <math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>F</mi></mrow></msub><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mo>/</mo><mi>p</mi></mrow></math> is non-zero. Much of this work was joint with Jacob Murre, and the article is dedicated to his memory.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 1","pages":"Pages 294-302"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145898101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Parshin’s method and the geometric Bombieri–Lang conjecture Parshin的方法和几何Bombieri-Lang猜想

IF 0.8 4区数学

Indagationes Mathematicae-New Series Pub Date : 2026-01-01 Epub Date: 2024-11-04 DOI: 10.1016/j.indag.2024.10.005

Finn Bartsch, Ariyan Javanpeykar

引用次数: 0

Generic motives and motivic cohomology of fields 域的一般动机与动机上同调

IF 0.8 4区数学

Indagationes Mathematicae-New Series Pub Date : 2026-01-01 Epub Date: 2025-08-05 DOI: 10.1016/j.indag.2025.07.006

F. Déglise

{"title":"Generic motives and motivic cohomology of fields","authors":"F. Déglise","doi":"10.1016/j.indag.2025.07.006","DOIUrl":"10.1016/j.indag.2025.07.006","url":null,"abstract":"<div><div>This paper investigates the structure of generic motives and their implications for the motivic cohomology of fields. Originating in Voevodsky’s theory of motives and related to Beilinson’s vision of a motivic <math><mi>t</mi></math>-structure, generic motives serve as pro-objects encoding essential information about cycles and cohomology. We present new computations of generic motives, focusing on curves and surfaces. These computations suggest a conjectural framework for morphisms of generic motives and highlight the central role of transcendental motives. We then focus on the motivic cohomology of fields, building on Borel’s rank computation of K-theory and its relation to higher regulators. We provide a direct argument for determining the weights in the <math><mi>λ</mi></math>-structure of the K-theory of number fields, bypassing the need for regulator maps. We show that motivic cohomology groups are often of infinite rank, typically matching the cardinality of the base field. For instance, we prove that motivic cohomology groups of <math><mi>R</mi></math> and <math><mi>ℂ</mi></math> are uncountable in many bi-degrees. Despite this, we propose a conjecture that complements the Beilinson–Soulé vanishing conjecture, suggesting that the growth of motivic cohomology is more controlled than these results may initially indicate.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 1","pages":"Pages 421-487"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145898104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Chow–Lefschetz motives 周-莱夫谢茨动机

IF 0.8 4区数学

Indagationes Mathematicae-New Series Pub Date : 2026-01-01 Epub Date: 2024-05-03 DOI: 10.1016/j.indag.2024.04.007

Bruno Kahn

引用次数: 0

Motives 动机

IF 0.8 4区数学

Indagationes Mathematicae-New Series Pub Date : 2026-01-01 Epub Date: 2024-09-24 DOI: 10.1016/j.indag.2024.09.008

Luca Barbieri-Viale

引用次数: 0

The Beauville–Voisin–Franchetta conjecture and LLSS eightfolds Beauville-Voisin-Franchetta猜想和LLSS八倍

IF 0.8 4区数学

Indagationes Mathematicae-New Series Pub Date : 2026-01-01 Epub Date: 2024-11-05 DOI: 10.1016/j.indag.2024.10.004

Robert Laterveer , Charles Vial

引用次数: 0

Universally defined cycles I 普遍定义循环I

IF 0.8 4区数学

Indagationes Mathematicae-New Series Pub Date : 2026-01-01 Epub Date: 2024-12-20 DOI: 10.1016/j.indag.2024.12.002

Claire Voisin

引用次数: 0

Dynamical systems for arithmetic schemes 算术方案的动力系统

IF 0.8 4区数学

Indagationes Mathematicae-New Series Pub Date : 2026-01-01 Epub Date: 2024-06-01 DOI: 10.1016/j.indag.2024.05.007

Christopher Deninger

引用次数: 0

K3 surfaces associated to a cubic fourfold 与立方四面体相关的 K3 表面

IF 0.8 4区数学

Indagationes Mathematicae-New Series Pub Date : 2026-01-01 Epub Date: 2024-09-02 DOI: 10.1016/j.indag.2024.08.003

Claudio Pedrini

{"title":"K3 surfaces associated to a cubic fourfold","authors":"Claudio Pedrini","doi":"10.1016/j.indag.2024.08.003","DOIUrl":"10.1016/j.indag.2024.08.003","url":null,"abstract":"<div><div>Let <math><mrow><mi>X</mi><mo>⊂</mo><msup><mrow><mi>P</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></math> be a smooth cubic fourfold. A well known conjecture asserts that <math><mi>X</mi></math> is rational if and only if there a Hodge theoretically associated K3 surface <math><mi>S</mi></math>. The surface <math><mi>S</mi></math> can be associated to <math><mi>X</mi></math> in two other different ways. If there is an equivalence of categories <math><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>≃</mo><msup><mrow><mi>D</mi></mrow><mrow><mi>b</mi></mrow></msup><mrow><mo>(</mo><mi>S</mi><mo>,</mo><mi>α</mi><mo>)</mo></mrow></mrow></math> where <math><msub><mrow><mi>A</mi></mrow><mrow><mi>X</mi></mrow></msub></math> is the Kuznetsov component of <math><mrow><msup><mrow><mi>D</mi></mrow><mrow><mi>b</mi></mrow></msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math> and <math><mi>α</mi></math> is a Brauer class, or if there is an isomorphism between the transcendental motive <math><mrow><mi>t</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow></mrow></math> and the (twisted ) transcendental motive of a K3 surface <math><mi>S</mi></math>. In this note we consider families of cubic fourfolds with a finite group of automorphisms and describe the cases where there is an associated K3 surface in one of the above senses.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 1","pages":"Pages 158-177"},"PeriodicalIF":0.8,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Bounding generators for the kernel and cokernel of the tame symbol for curves 为曲线的驯服符号的核和核的边界生成器

IF 0.8 4区数学

Indagationes Mathematicae-New Series Pub Date : 2026-01-01 Epub Date: 2024-11-06 DOI: 10.1016/j.indag.2024.11.002

Rob de Jeu

引用次数: 0