Hyperdescent and etale K-theory

• 成果类型: Article
• 署名作者: Clausen, Dustin; Mathew, Akhil
• 署名单位: University of Copenhagen; University of Chicago
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01043-3
• 发表日期: 2021
• 页码: 981-1076
• 关键词: equivariant stable-homotopy; HOMOLOGY; descent; localization; COHOMOLOGY; hochschild; ALGEBRAS

摘要

We study the etale sheafification of algebraic K-theory, called etale K-theory. Our main results show that etale 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 etale 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 etale sites.