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Akhil Mathew (November 6, 2020): Etale K-theory and motivic cohomology
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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).
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).