Geodesic
The $\text{K}$-theory of perfectoid rings
Documenta mathematica, Tome 27 (2022), pp. 1923-1951 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/dm/x22
Classification : 14G45, 19D50
Mots-clés : algebraic K-theory, perfectoid rings 
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     author = {Ben Antieau and Akhil Mathew and Matthew Morrow},
     title = {The $\text{K}$-theory of perfectoid rings},
     journal = {Documenta mathematica},
     pages = {1923--1951},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x22},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x22/}
}
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Ben Antieau; Akhil Mathew; Matthew Morrow. The $\text{K}$-theory of perfectoid rings. Documenta mathematica, Tome 27 (2022), pp. 1923-1951. doi: 10.4171/dm/x22

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