Cohomology of sheaves and schemes

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Cohomology of sheaves and schemes

Semester
SoSe 2026

Lecturer
Marc Hoyois

Type of course (Veranstaltungsart)
Seminar

German title
Kohomologie der Garben und der Schemata

Contents
In this seminar, we will introduce the cohomology of sheaves on topological spaces and schemes
following Chapter III of Hartshorne. Beyond the definitions and basic properties of sheaf
cohomology, we will compute the cohomology of affine schemes and projective spaces, and we will
discuss the Serre duality theorem for projective schemes and its connection to the residue theorem
in complex analysis. The first few talks are about sheaves on topological spaces and do not require
any background in algebraic geometry. The remaining talks assume some basic knowledge of schemes.
See the course homepage for a detailed program.

Time/Date
Wednesday 16-18

Location
M104

Course homepage
https://hoyois.app.uni-regensburg.de/SS26/sheafcoh/index.html
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Organisational meeting/distribution of topics: First week of the semester, or by email
beforehand
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
BSem, MV, MSem, BSem.2, BSem.3

ECTS
4,5