Foundations of Logarithmic Adic Spaces

2017/09/18 by Hansheng Diao, Diao, Hansheng
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1709.05781

openalex publication_date 2017/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \mathbbF_p-local systems on proper log smooth adic spaces.

Citations

• Relative p-adic Hodge theory: Foundations

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