拓扑Hochschild同调的导出不变量

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-06-28 DOI:10.14231/ag-2022-011

Benjamin Antieau, Daniel Bragg

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引用次数: 7

摘要

我们考虑由拓扑Hochschild同调产生的具有正特征的变种的导出不变量。利用Ekedahl和Illusie Raynaud在研究斜率谱序列时提出的理论，我们研究了与Hodge-Witt和结晶上同调群有关的各种$p$-二元量在导出等价下的行为，包括斜率数、多米诺数和Hodge-Wwitt数。因此，我们得到了导出等价变种的Hodge数的限制，将Popa-Schell的结果部分推广到了正特征。

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Derived invariants from topological Hochschild homology

We consider derived invariants of varieties in positive characteristic arising from topological Hochschild homology. Using theory developed by Ekedahl and Illusie-Raynaud in their study of the slope spectral sequence, we examine the behavior under derived equivalences of various $p$-adic quantities related to Hodge-Witt and crystalline cohomology groups, including slope numbers, domino numbers, and Hodge-Witt numbers. As a consequence, we obtain restrictions on the Hodge numbers of derived equivalent varieties, partially extending results of Popa-Schell to positive characteristic.

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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.