Hyperdescent and étale K-theory

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 w...

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Bibliographic Details
Published inInventiones mathematicae Vol. 225; no. 3; pp. 981 - 1076
Main Authors Clausen, Dustin, Mathew, Akhil
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021
Springer Nature B.V
Subjects
Algebra
Mathematics
Mathematics and Statistics
Sheaves
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Summary: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.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-021-01043-3