The K-theory of perfectoid rings

2022/03/12 by Antieau, Benjamin, Mathew, Akhil, Morrow, Matthew · 2 citations
#FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2203.06472

Abstract

We establish various properties of the p-adic algebraic K-theory of smooth algebras over perfectoid rings living over perfectoid valuation rings. In particular, the p-adic K-theory of such rings is homotopy invariant, and coincides with the p-adic K-theory of the p-adic generic fibre in high degrees. In the case of smooth algebras over perfectoid valuation rings of mixed characteristic the latter isomorphism holds in all degrees and generalises a result of Nizioł.

Cited by

• Equivariant localizing invariants of simple varieties
• Beilinson--Lichtenbaum phenomenon for motivic cohomology

Related

• Purity for Perfectoidness
• K-Theory of Cuspidal Curves Over a Perfectoid Base And Formal Analogues
• Perfectoid Spaces in Multivariate p-adic Hodge Theory
• Perfectoidness via Sen Theory and Applications to Shimura Varieties
• On the K-theory of the p-adic unit disk