Perfectoid Banach ring and tilting equivalence.

Time: 14:00-15:45, 05/03/2026 (Thursday)

Venue: Room 612, A6, Institute of Mathematics-VAST

Online (Join Zoom Meeting) link: https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1

Abstract: After introducing the definition and some basic properties of perfectoid rings (follow
[BMS]), we present the Kedlaya–Liu tilting equivalence for Banach perfectoid rings, which provides an analytic formulation of Scholze’s tilting theory suited to relative p-adic Hodge theory. In this framework, Banach perfectoid rings of mixed characteristic (0,p) are equivalent to Banach perfectoid rings (perfect ring) of characteristic p via the tilting functor with inverse given by a Witt vector untilting construction. The equivalence preserves uniformity, completeness, rational localizations, and finite étale morphisms, and is functorial with respect to Banach algebra morphisms. This analytic version of tilting serves as a foundational tool for relative p-adic Hodge theory, allowing problems in mixed characteristic to be systematically reduced to characteristic p while retaining full geometric and cohomological information.

References:

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2. [Ce19] Česnavičius. Purity for the Brauer group, Duke Mathematical Journal Vol. 168, No. 8, 2019
3. [KL15] Kedlaya and R. Liu, Relative p-adic Hodge theory: Foundations, Astérisque 371,Soc. Math. France, Paris,2015.