# \'Etale K-theory and motivic cohomology

*Akhil Mathew (University of Chicago)*

**06-Nov-2020, 20:00-21:00 (4 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

**Stanford algebraic geometry seminar **

**Series comments: **The seminar was online for a significant period of time, but for now is solely in person.
More seminar information (including slides and videos, when available): agstanford.com

Organizer: | Ravi Vakil* |

*contact for this listing |