The K-theory of perfectoid rings
K-Theory and Homology
2022-03-15 v1
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 Nizio{\l}.
Keywords
Cite
@article{arxiv.2203.06472,
title = {The K-theory of perfectoid rings},
author = {Benjamin Antieau and Akhil Mathew and Matthew Morrow},
journal= {arXiv preprint arXiv:2203.06472},
year = {2022}
}
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