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2019 On the $p$-typical de Rham–Witt complex over $W(k)$
Christopher Davis
Algebra Number Theory 13(7): 1597-1631 (2019). DOI: 10.2140/ant.2019.13.1597

Abstract

Hesselholt and Madsen (2004) define and study the (absolute, p-typical) de Rham–Witt complex in mixed characteristic, where p is an odd prime. They give as an example an elementary algebraic description of the de Rham–Witt complex over (p), WΩ(p). The main goal of this paper is to construct, for k a perfect ring of characteristic p>2, a Witt complex over A=W(k) with an algebraic description which is completely analogous to Hesselholt and Madsen’s description for (p). Our Witt complex is not isomorphic to the de Rham–Witt complex; instead we prove that, in each level, the de Rham–Witt complex over W(k) surjects onto our Witt complex, and that the kernel consists of all elements which are divisible by arbitrarily high powers of p. We deduce an explicit description of WnΩA for each n1. We also deduce results concerning the de Rham–Witt complex over certain p-torsion-free perfectoid rings.

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Christopher Davis. "On the $p$-typical de Rham–Witt complex over $W(k)$." Algebra Number Theory 13 (7) 1597 - 1631, 2019. https://doi.org/10.2140/ant.2019.13.1597

Information

Received: 22 June 2017; Revised: 21 April 2019; Accepted: 13 June 2019; Published: 2019
First available in Project Euclid: 16 January 2020

zbMATH: 1423.13113
MathSciNet: MR4009672
Digital Object Identifier: 10.2140/ant.2019.13.1597

Subjects:
Primary: 13F35
Secondary: 13N05 , 14F30

Keywords: de Rham–Witt complex , perfectoid rings , Witt vectors

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 7 • 2019
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