We kindly ask all participants, including remote ones and those
watching recorded videos, to register at this link.
The goal of the seminar is a quick introduction to algebraic $K$-theory with
applications in algebraic geometry and algebra. We plan to consider several approaches
to algebraic $K$-groups, mainly in the context of exact categories, and also to analyze
concepts and constructions in algebraic geometry related to algebraic $K$-theory. The
apotheosis of the seminar should be a detailed study of a proof of the famous
Merkuryev-Suslin theorem which relates Milnor $K$-groups and Brauer groups of fields.
Talks will be given mainly by undergraduate and graduate students participating
in the seminar. As for preliminaries, familiarity with algebra and algebraic geometry,
homotopy theory, category theory, and a little homological algebra will be required.
Program
- Grothendieck groups, explicit definition of $K_0, K_1, K_2$ for rings.
- Milnor $K$-groups, Moore-Matsumoto theorem.
- Plus construction, $Q$-construction, Waldhausen $S$-construction.
- Comparison of various definitions of higher $K$-groups.
- General properties of algebraic $K$-groups.
- $K$-theory of schemes, $K$-cohomology.
- Brown-Gersten spectral sequence, Gersten conjecture.
- The Merkuryev-Suslin theorem.
 RSS: Forthcoming seminars
 Seminar organizers
Gorchinskiy Sergey Olegovich
Fonarev Anton Vyacheslavovich
Organizations
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center |
