\'Etale K-theory and motivic cohomology

Akhil Mathew (University of Chicago)

06-Nov-2020, 20:00-21:00 (2 years ago)

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).

algebraic geometry

Audience: researchers in the topic

( slides | video )

Stanford algebraic geometry seminar

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Organizer: Ravi Vakil*
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