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Fakultät für Mathematik Universität Regensburg
Selmer K-theory
Semester
SoSe 2023

Lecturer
Marc Hoyois

Type of course (Veranstaltungsart)
Oberseminar

German title
Selmer-K-Theorie

Contents
Selmer K-theory is a localizing invariant of stable categories introduced by Clausen to give a
K-theoretic construction of the Artin map from the idele class group of a number field to its
abelianized Galois group. For schemes, Selmer K-theory is closely related to the étale
sheafification of algebraic K-theory, and in general it can thus be viewed as a non-commutative
extension of the latter. In this seminar, we will review the definition of Selmer K-theory, which
combines insights of Thomason on K(1)-local algebraic K-theory and of Geisser-Hesselholt on
topological cyclic homology. We will then discuss applications to étale K-theory following
Clausen and Mathew.

Literature
D. Clausen and A. Mathew, "Hyperdescent and étale K-theory"; D. Clausen, "A
K-theoretic approach to Artin maps"

Time/Date
Tue 14-16

Location
tba and online

Course homepage
https://hoyois.app.uni-regensburg.de/SS23/ksel/index.html
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Presentation: Giving a seminar talk of roughly 90 minutes
Examination (Prüfungsleistungen)
  • Detailed written report of the seminar talk
Modules
MV, MSem

ECTS
4,5