Seminar: Introduction to Algebraic K-theory (Winter Semester 26/27)

Syllabus

Assumed prerequisites

Some familiarity with the basics of homotopy theory and higher category theory, as would be covered in last term's Topologie IV course, the notes for which can be made available upon request. You may also find some benefit in brushing up on the first and fourth chapters of this textbook which is currently being written by Dr. Bastiaan Cnossen, whose website you may otherwise find useful to peruse.

Overview

We expect to cover the following topics over the course of this seminar.
Topic Summary No. of talks
Semiadditivity, Additivity, Group Completion \(\mathrm{Cat^{sadd}},\ \mathrm{Cat^{add}}\), smashing localizations and group completion \(K\)-theory (including \(KU\)) 2 talks
\(K(\mathbb{F}_{p})\) Adams operations, Brauer lifting, \(H^{\ast}(\mathrm{GL}_{n}(\mathbb{F}_{p}))\) following Quillen 4 talks
\(K\)-theory of stable \(\infty\)-categories Additive and localizing invariants, noncommutative motives, universality (without proof) 2 talks
Additional topics, TBD, will be populated 4 talks