The goal of this seminar is to study Quillen's computation of the algebraic K-theory of finite fields. This makes use of various topological and algebraic tools from homological algebra, simplicial homotopy theory, topological K-theory and group cohomology. These tools will be reviewed in as much detail as possible and depending on the audience's prior knowledge. 

Quillen - On the Cohomology and K-Theory of the General Linear Groups Over a Finite Field
Quillen - Higher Algebraic K-theory: I
Srinivas - Algebraic K-theory
Weibel - The K-book
Mitchell - Notes on the K-theory of finite fields
Hebestreit - Notes for Algebraic and Hermitian K-Theory (https://drive.google.com/file/d/1UDstSSvvKi7liH3-DOa3YbMLUCp_BAtT/view)

Basic background knowledge of algebraic topology and homological algebra will be assumed. While no prior knowledge of algebraic K-theory or group cohomology is required, some basic familiarity with these areas, perhaps gained from courses in the recent winter semester, would be desirable. 

• Organisational meeting/distribution of topics: Per email at: giacomo.bertizzolo "at"
  mathematik.uni-regensburg.de
• Registration for course work/examination/ECTS: FlexNow

• Presentation: Giving a seminar talk of roughly 90 minutes

• Detailed written report of the seminar talk