Derived Categories

Derived Categories

Semester
SoSe 2022

Lecturer
Denis-Charles Cisinski

Type of course (Veranstaltungsart)
Vorlesung

Contents
These lectures will be a continuation of the course on "Derived functors and cohomology through
higher categories". We will focus on stable categories, seen as enhanced versions of derived
categories. After a few preliminaries, we will in particular study the following aspects: derived
Morita theory (Fourier-Mukai functors), perfect complexes, t-structures and metrics on stable
infinity-categories. Using Neeman's notion of approximable triangulated categories, we will study
representability theorems in bounded derived categories of coherent sheaves on noetherian schemes.

Recommended previous knowledge
We will use the language of infinity-category theory freely. Eventually, some basic knowledge of
algebraic geometry (e.g. the definition of quasi-coherentsheaves on a scheme) will help.

Time/Date
Mo 16-18, Fri 16-18

Location
M 103 and online

Course homepage
http://www.mathematik.uni-regensburg.de/cisinski/lehre.html
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Preliminary registration for the organisation of exercise classes: at the end of the previous
semester via EXA or LSF (see announcement by the department)
Registration for the exercise classes: via GRIPS
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Successful participation in the exercise classes:

Examination (Prüfungsleistungen)

Oral exam: Duration: 30 min., Date: by appointment, re-exam: Date:

Modules
BV, MV, MArGeo, MGAGeo, LA-GyGeo

ECTS
9