\'Etale K-theory and motivic cohomology
Akhil Mathew (University of Chicago)
Abstract: Two key features of algebraic K-theory are its failure to satisfy \'etale descent, and its motivic filtration in terms of higher Chow groups in the case of smooth schemes over a field (but expected more generally). I will explain a description of \'etale K-theory, which is the universal approximation to K-theory that satisfies \'etale descent; this is joint work with Dustin Clausen. Moreover, following the recent work of Bhatt--Morrow--Scholze on topological cyclic homology, I will also explain a construction of (an analog of) the motivic filtration on \'etale K-theory (and \'etale motivic cohomology) for arbitrary schemes (work in progress with Bhargav Bhatt and Dustin Clausen).
Audience: researchers in the topic
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