Topological cyclic homology and the Fargues-Fontaine curve
Lars Hesselholt
TL;DR
This paper explains how topological cyclic homology relates to the Fargues-Fontaine curve, revealing its structure through the decomposition into a punctured curve and a formal neighborhood, connecting algebraic topology with p-adic geometry.
Contribution
It provides an expository account of the connection between topological cyclic homology and the geometric structure of the Fargues-Fontaine curve, highlighting their natural interplay.
Findings
Fargues-Fontaine curve arises from topological cyclic homology
Decomposition into punctured curve and formal neighborhood explained
Links between algebraic topology and p-adic geometry established
Abstract
The purpose of this expository paper is to explain how the Fargues-Fontaine curve and its decomposition into a punctured curve and the formal neighborhood of the puncture naturally arise from various forms of topological cyclic homology and maps between them.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology