TR with logarithmic poles and the de Rham-Witt complex

2024/12/01 by Andriopoulos, Faidon
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2412.00929

Abstract

In the article of Hesselholt [Hes05], a set of conjectures is laid out. Given a smooth scheme X over the ring of integers O_K of a p-adic field K, these conjectures concern the expected relation between log topological restriction homology TR^r (X,M_X) and the absolute log de Rham--Witt complex W_rΩ_(X,MX). In this note, which is companion to [And24a], we discuss the case of a p-completely smooth p-adic formal scheme X over spf O_C, where C is the field of p-adic complex numbers. Along the way, we study the motivic filtration of log TR^r and its S¹-homotopy fixed points, following ideas of [Bin+23].

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