#### Lecture series and student seminars October 21 – February 22

**Time**: Tuesday 10 -12, Friday 10- – 12

**Location**: Mainz

**Online coordinates**: none

This lecture is a continuation of the lecture Algebraic Geometry 1. It deals with local and global properties of scheme morphisms and the cohomology of schemes, in particular, techniques from homological algebra and derived functors, cohomology of affine schemes and projective space, duality.

**Time**: Monday 11:40 – 13:20

**Location**: Darmstadt

**Online coordinates**: Please contact one of the lecturers.

**Time**: Monday 10 – 12, Thursday 10 – 12

**Location**: Mainz

**Online coordinates**: none

Foundations on algebraic number fields: Integral extensions, ideals, Dedekind domains, prime ideal decomposition, Minkowski theory, class number, Dirichlet’s unit theorem, quadratic and cyclotomic number fields, extension of Dedekind domains, localization, valuations, extension of valuations, Galois theory of valuations, Hilbert’s ramification theory

**Time**: Wednesday 11 – 13, Friday 9 – 11

**Location**: Heidelberg, Mathematikon, INF 205, SR A

**Online coordinates**: none

The lecture is a continuation of the course Algebraic Number Theory 1 of the previous term. The main topic and goal is

Galois cohomology. Topics: derived functors, group cohomology, profinite groups, infinite Galoistheory, local fields, local Tate-duality, local class field theory.

**Time**: Monday 14 – 16, Wednesday 14-16

**Location**: Frankfurt, Hörsaaltrakt Campus Bockenheim Mondays H15, Wednesdays H13

**Online coordinates**: none

**Time**: Thursday 12 – 14

**Location**: Frankfurt, Robert-Mayer-Str. 6-8, Raum 308

**Online coordinates**: Please send an email to me to receive the zoom

link.

**Time**: Monday 10 – 12

**Location**: Mainz

**Online coordinates**: via MS Teams. Please send an email to Georg Tamme to enrol in this course.

Linear algebraic groups are an important class of groups that come with the structure of an algebraic variety. Examples include the general linear group, the special linear group or the orthogonal group over a field. In this seminar, we will develop the foundations of the theory of linear algebraic groups. We will discuss the basic definitions, important subgroups such as tori and Borel subgroups, the relationship between a linear algebraic group and its Lie algebra, as well as the root datum of a linear algebraic group. The endpoint of the seminar will be a discussion of the classification of reductive groups.

**Time**: tba

**Location**: tba

**Online coordinates**: tba

The aim is to study Deligne’s article “Cohomology étale: le point de depart” in SGA 4 1/2 and to provide the necessary background. Participants are expected to have knowledge of a 2 semester course of Algebraic Geometry.

**Time**: Wednesday and Friday 11-13, Exercises: Monday 14-16 (tentative)

**Location**: Heidelberg, Mathematikon

**Online coordinates**: none

In Heidelberg we are organizing a seminar on **Tame cohomology** following an article by the PIs Katharina Hübner and Alexander Schmidt. The program is organized by Katharina Hübner.

**Time**: Wednesdays 9:30-11:00

**Location**: Heidelberg, Mathematikon

**Online coordinates**: none

Some of the lectures are in German. Please contact the lecturer if in doubt.