有限域上的非代数几何琐碎同调类

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-07 DOI:10.1016/j.aim.2024.109964

Federico Scavia , Fumiaki Suzuki

引用次数: 0

摘要

我们给出了有限域 F 上的光滑投影变项 X 的第一个例子，该投影变项承认一个在 F‾ 上消失的 4 度非代数扭转 ℓ-adic 同调类。我们用它们来证明在 F 上的积分泰特猜想的两个版本并不等同，而且科利奥-泰莱与卡恩的基本精确序列并不一定分裂。我们的一些例子维数为 4，是已知的第一个 Hnr3(X,Q2/Z2(2))不求和的四折的例子。

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Non-algebraic geometrically trivial cohomology classes over finite fields

We give the first examples of smooth projective varieties X over a finite field

F

admitting a non-algebraic torsion ℓ-adic cohomology class of degree 4 which vanishes over

\overline{F}

. We use them to show that two versions of the integral Tate conjecture over

F

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

H_{nr}^{3} (X, Q_{2} / Z_{2} (2))

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.