Perfectoid Spaces in Multivariate p-adic Hodge Theory

2025/08/25 by Pal, Aprameyo, Pokhrel, Rohit
#11S37 #12J25 #14G17 #14G20 #14G45 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.18198

Abstract

Perfectoid spaces have become a crucial tool in p-adic geometry, serving as a bridge between adic spaces in characteristic 0 and those in characteristic p. In this article, we develop a systematic way to study the structure of perfectoid spaces within the setting of multivariate p-adic Hodge theory over a variant of the rings introduced in \citeBri.

Citations

• Multivariable p-adic Hodge theory for products of Galois groups
• On Bloch-Kato Selmer groups and Iwasawa theory of p-adic Galois representations
• Cohomology and overconvergence for representations of powers of Galois groups
• Stably uniform affinoids are sheafy
• Perfectoid spaces

Related

• The K-theory of perfectoid rings
• A Berkovich Approach to Perfectoid Spaces
• Period Rings with Big Coefficients and Applications I
• A Cartesian Diagram of Rapoport-Zink Towers over Universal Covers of p-Divisible Groups
• Topics on Geometric and Representation Theoretic Aspects of Period Rings I