## Lecture: Lubin-Tate Spaces - Sommersemester 2021

Contact:

Dr. Johannes Anschütz

Endenicher Allee 60 · Zimmer 4.027

**Tel.:** 0228-73-62216

** E-mail: ja **(ergänze @math.uni-bonn.de)

In summer term 2021 I will be a teaching substitute for Prof. Dr. Eva Viehmann at the TU München. As the lecture will be held online students other universities are welcome, too.

## Time and Place

Dates for the lectures (MESZ): Mondays, 14:15-15:45h, Wednesday, 14:15-15:45h.

First Lecture: 12.4.2021.

The lecture will take place via Zoom. To receive the meeting number and password write me an email.

Unfortunately, the exercise session today (2.7.2021) has to be cancelled on short notice!

## Content of the course

The aim of this course is to discuss local class field theory following Lubin-Tate and to provide a gentle introduction to rigid analytic geometry, with the motivating example being by Lubin-Tate spaces. For the latter we will follow mostly the paper "Equivariant vector bundles on the Lubin-Tate moduli space" by Gross and Hopkins.

## Prerequisites

For the first part of the course, knowledge of basic algebra (rings, ideals, groups, modules, ..) and category theory (functors, natural transformations,...) is necessary. Knowledge of local fields or completions of rings will be helpful, but is not mandatory as we will recall the necessary facts in the course.
For the second part knowledge of algebraic geometry (projective spaces, coherent sheaves,...) will be helpful, but not mandatory.

## Lecture notes

TeXed lecture notes are prepared in parallel to the lectures.

## Literature

- Gross, Hopkins: Equivariant vector bundles on the Lubin-Tate moduli spaces,
- Lubin, Tate: Formal complex multiplication in local fields,
- Lubin, Tate: Formal moduli of one-dimensional formal Lie groups,
- Stacks Project, Chapter Formal deformation theory,
- Wedhorn, Torsten: Adic spaces

## Exercise sessions

Date for the exercise session: Fridays, 14:15-15:45h.

First exercise session: 16.4.2021.

There will be exercise sessions accompanying the lecture and participating in those is mandatory for taking the oral exam. The content of the exercise sessions will be a mixture of discussing the lecture and solving exercises in presence. We use the same Zoommeeting for exercise session as for the lecture.

## Exams

Students registered at the TU München can take oral exams (via Zoom). In case you want to take the exam, please register online for the first episode of exams (19.7.-23.7.) or the second (27.9.-30.9.). In either case, send me an email to arrange the date of the exam.

*Last modified: March 2021, Johannes Anschütz*

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