English

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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