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arXiv · 1709.05781

Foundations of Logarithmic Adic Spaces

Hansheng Diao
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Abstract

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

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Hansheng Diao. 2017-09-18. Foundations of Logarithmic Adic Spaces. https://arxiv.org/abs/1709.05781

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