Akhil Mathew (November 6, 2020):  Etale K-theory and motivic cohomology
Channel: Algebraic Geometry at Stanford
Date: 2021-03-09

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).