Hyperdescent and étale K-theory

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We study the étale sheafification of algebraic K-theory, called étale K-theory. Our main results show that étale K-theory is very close to a noncommutative invariant called Selmer K-theory, which is defined at the level of categories. Consequently, we show that étale K-theory has surprisingly well-behaved properties, integrally and without finiteness assumptions. A key theoretical ingredient is the distinction, which we investigate in detail, between sheaves and hypersheaves of spectra on étale sites.

OriginalsprogEngelsk
TidsskriftInventiones Mathematicae
Vol/bind225
Udgave nummer3
Sider (fra-til)981-1076
Antal sider96
ISSN0020-9910
DOI
StatusUdgivet - sep. 2021

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Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

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