Algebraic K-theory

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Algebraic K-theory

Semester
SoSe 2025

Lecturer
Marc Hoyois

Type of course (Veranstaltungsart)
Vorlesung

German title
Algebraische K-Theorie

Contents
Algebraic K-theory was invented by Grothendieck in the 1950s in his proof of the
Grothendieck–Riemann–Roch theorem. Nowadays algebraic K-theory plays an important role
in various fields of mathematics, notably algebraic number theory, algebraic geometry, homotopy
theory, and geometric topology. In particular, it appears in the formulation of many deep
conjectures. In this course, we will introduce the algebraic K-theory of rings, starting with
elementary definitions of K_0 and K_1 and making our way to Quillen's construction of higher
algebraic K-theory.

Recommended previous knowledge
Commutative algebra, category theory

Time/Date
Tue/Thu 8-10

Location
M101

Course homepage
https://hoyois.app.uni-regensburg.de/SS25/ktheory/index.html
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Successful participation in the exercise classes: 50% of the points

Examination (Prüfungsleistungen)

Oral exam: Duration: 30 minutes, Date: individual appointments, re-exam: Date: tbd

Modules
BV, MV, MArGeo, MGAGeo

ECTS
9