Motivic cohomology of schemes

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Motivic cohomology of schemes

Semester
SoSe 2026

Lecturer
Marc Hoyois, Marco Volpe

Type of course (Veranstaltungsart)
Oberseminar

German title
Motivische Kohomologie der Schemata

Contents
The goal of this seminar is to understand the motivic filtration of the A^1-invariant algebraic
K-theory of arbitrary schemes and the resulting theory of A^1-invariant motivic cohomology, recently
developed in this generality by Bachmann, Elmanto, and Morrow. The construction uses many aspects of
the formalism of motivic spectra, including the slice filtration, the six-functor formalism, and
framed correspondences, which we will review. We will then discuss the comparison with
cycle-theoretic constructions in special cases (for smooth schemes over Dedekind rings), with
syntomic cohomology (the Beilinson-Lichtenbaum conjecture), and compute motivic cohomology in low
weights.

Literature
Tom Bachmann, Elden Elmanto, Mathew Morrow: A^1-invariant motivic cohomology of schemes

Time/Date
Tuesday 14-16

Location
M311

Course homepage
https://hoyois.app.uni-regensburg.de/SS26/motiviccoh/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