Bonn Topology Group - Abstracts

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Talk

June 19th 2018
Christopher Davis (University of California, Irvine, USA): On the absolute de Rham-Witt complex over W(k) and over perfectoid rings

Abstract

In characteristic p, the de Rham-Witt complex was introduced by Bloch, Deligne and Illusie. A relative version in mixed characteristic was introduced by Langer and Zink, and an absolute version in mixed characteristic was introduced by Hesselholt and Madsen. In this talk, we focus on the absolute version; it is closely related to the spectrum TR. Our main goal is to sketch a proof that when A is a perfectoid ring and is p-torsion free, then the p-adic Tate module of W_n\Omega^1_A is a free W_n(A)-module of rank one. This is very related to work of Hesselholt and of Bhatt-Morrow-Scholze, although the proof we discuss is more algebraic and less topological in nature.
This is ongoing joint work with Irakli Patchkoria.

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