Algebraic Morava K-theory

Record

Yes

Abstract

This mini-course focuses on Quillen's approach to cobordism theories and the adaptation of these ideas in the context of algebraic geometry. We will discuss how formal group laws are related to generalized cohomology theories, stack of formal groups and Morava K-theories.

Reference

D. Quillen, "Elementary proofs of some results of cobordism theory using Steenrod operations", Advances in Mathematics 7:1 (1971) 29-56.

D. Ravenel, "Complex cobordism and stable homotopy groups of spheres", Academic Press Orland (1986) reprinted as: AMS Chelsea Publishing 347 (2004).

M. Levine, F. Morel, "Algebraic Cobordism", Springer Monographs in Mathematics, Springer-Verlag Berlin Heidelberg (2007).

A. Vishik, "Stable and unstable operations in algebraic cobordism", Annales Scientifiques de l'Ecole Normale Superieure 52:3 (2019) 561-630.

Audience

Graduate

Prerequisite

Algebraic topology, algebraic geometry

Lecturer Intro

Andrei Lavrenov got his undergraduate education in St. Petersburg where he graduated from St. Petersburg State University. He got his PhD from Ludwig Maximilian University of Munich, where he is working now. His research interests include algebraic groups, generalized cohomology theories and motives.