Revisiting the de Rham-Witt complex

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2018-05-15 DOI:10.24033/ast.1146

B. Bhatt, J. Lurie, A. Mathew

引用次数: 25

Abstract

The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p$. We introduce a category of cochain complexes equipped with an endomorphism $F$ (of underlying graded abelian groups) satisfying $dF = pFd$, whose homological algebra we study in detail. To any such object satisfying an abstract analog of the Cartier isomorphism, an elementary homological process associates a generalization of the de Rham-Witt construction. Abstractly, the homological algebra can be viewed as a calculation of the fixed points of the Berthelot-Ogus operator $L \eta_p$ on the $p$-complete derived category. We give various applications of this approach, including a simplification of the crystalline comparison in $A \Omega$-cohomology theory.

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本文的目标是在特征$p$的完美域上提供光滑变种的de Rham Witt复形的新构造。我们引入了一类具有满足$dF=pFd$的自同态$F$（底层分次阿贝尔群）的共链复形，我们详细研究了它的同调代数。对于任何满足Cartier同构抽象类似的对象，一个初等同源过程将de Rham Witt构造的推广联系起来。抽象地说，同调代数可以看作是Bertelot-Ogus算子$L\eta_p$在$p$-完全派生范畴上的不动点的计算。我们给出了这种方法的各种应用，包括$a\Omega$-上同调理论中晶体比较的简化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.