Foundations of Logarithmic Adic Spaces

Abstract

The main objects of study are adic spaces with logarithmic structures. After establishing the basic definitions, we analyze the Kummer étale and pro-Kummer étale topologies on log adic spaces. In particular, we show that log adic spaces are locally "log affinoid perfectoid" in the pro-Kummer étale topology. As an application, we prove finiteness of cohomologies for Kummer étale ${\mathbb{F}}_p$-local systems on proper log smooth adic spaces.

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References in corpus (1)

• Relative p-adic Hodge theory: Foundations

Cited by in corpus (1)

• Logarithmic de Rham comparison for open rigid spaces