## Anabelian geometry seminar

Together with Harry Smit I am organizing a seminar on anabelian geometry. The aim is to go through the following papers together

- Neukirch - Kennzeichnung der p-adischen und der endlichen algebraischen Zahlkörper (English exposition in "Cohomology of Number Fields", Chapter 12).
- Uchida - Isomorphisms of Galois groups of solvably closed Galois extensions.
- Saidi, Tamagawa - The m-step solvable anabelian geometry of number fields.

The first paper shows that a number field is determined by its absolute Galois group. The second paper strengthens this result by proving that the Galois group of the solvable closure still determines the number field. Both these papers should be accessible to any number theorist. The third paper is a recent result and shows that one only needs to take the 3-step solvable closure. It would be great if we could understand this result, but also think about extensions to the 2-step closure. The current schedule is as follows

- (Peter): "Black box" talk: an overview of the Neukirch-Uchida theorem (Section 12.1 NSW), assuming black boxes for local and global cohomology. Slides
- (Harry): Cohomology of local fields (e.g. Chapter 7 in NSW).
- (Axel): Cohomology of global fields (bits of Chapter 8 and Chapter 9 in NSW).
- (Zhizhong): Section 12.2.
- (Carlo): Talks on what happens if you change to the solvable closure.

## Seminar on the work of Alexander Smith

Together with Carlo Pagano I gave a seminar on the work of

Alexander Smith.

Lecture 1: Friday 5 October 2018 10:00-12:00 (Carlo Pagano)

Lecture 2: Friday 12 October 2018 10:00-12:00 (Carlo Pagano)

Lecture 3: Friday 19 October 2018 10:00-12:00 (Peter Koymans)

Lecture 4: Friday 2 November 2018 09:00-11:00 (Peter Koymans)

Lecture 5: Tuesday 27 November 2018 11:00-13:00 (Carlo Pagano)

Lecture 6: Monday 3 December 2018 11:00-13:00 (Carlo Pagano)

The material in each lecture depends in a crucial way on the material in the previous lectures. The seminar was filmed. If one is interested in the video material, send an e-mail to me. Due to its success the seminar continued in a more informal setting.

Lecture 7: Thursday 7 February 2019 14:00-16:00 (Peter Koymans)

Lecture 8: Monday 25 March 2019 15:30-17:30 (Peter Koymans)

Lecture 9: Monday 8 April 2019 15:30-17:30 (Peter Koymans)

Lecture 10: Monday 20 May 2019 14:00-17:00 (Peter Koymans)

Recently, I have given some talks at a small informal seminar in Michigan. The slides can be found here.

Talk 1
Talk 2
Talk 3