Geodesic
The $\text{K}$-theory of perfectoid rings
Documenta mathematica, Tome 27 (2022), pp. 1923-1951.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We establish various properties of the $p$-adic algebraic $\text{K}$-theory of smooth algebras over perfectoid rings living over perfectoid valuation rings. In particular, the $p$-adic $\text{K}$-theory of such rings is homotopy invariant, and coincides with the $p$-adic $\text{K}$-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.
Classification : 19D50, 14G45
Keywords: algebraic \(K\)-theory, perfectoid rings 
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     title = {The {\(\text{K}\)-theory} of perfectoid rings},
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Antieau, Ben; Mathew, Akhil; Morrow, Matthew. The \(\text{K}\)-theory of perfectoid rings. Documenta mathematica, Tome 27 (2022), pp. 1923-1951. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a17/