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 ho-motopy 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 per-fectoid valuation rings of mixed characteristic the latter isomorphism holds in all degrees and generalises a result of Nizioł.
Original language | English (US) |
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Pages (from-to) | 1923-1952 |
Number of pages | 30 |
Journal | Documenta Mathematica |
Volume | 27 |
DOIs | |
State | Published - 2022 |
Funding
We thank Dustin Clausen, Lars Hesselholt, and Wiesława Nizioł for helpful discussions. This material is based upon work supported by the National Science Foundation under Grant No. DMS-1440140 while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2019 semester. The first author was supported by NSF Grants DMS-2102010 and DMS-2120005 and a Simons Fellowship. This work was done while the second author was a Clay Research Fellow. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 101001474).
Keywords
- algebraic K-theory
- perfectoid rings
ASJC Scopus subject areas
- General Mathematics