GRK-Seminar Sommersemester 2025

RTG Seminar Summer term 2025

The Thursday morning seminar (10:15-11:45 in WSC-N-U-3.05) will be the “Research Training Group Seminar” where members of the RTG (PhD students, post-docs,…) present their results. Sometimes, we also have speakers from other places. Depending on the number of speakers and on the proposed topic, a speaker could use one or two sessions.

24.04.2025	Gautier Ponsinet	On a characterisation of perfectoid fields by Iwasawa theory
08.05.2025	Wiesława Nizioł	Understanding p-adic etale cohomology of varieties 1 (Mercator lecture)
09.05.2025, 14:15	Wiesława Nizioł	Understanding p-adic etale cohomology of varieties 2 (Mercator lecture)
15.05.2025	Johannes Sprang	Algebraicity and p-adic interpolation of critical Hecke L-values
22.05.2025	Wiesława Nizioł	Understanding p-adic etale cohomology of varieties 3 (Mercator lecture)
23.05.2025, 14:15	Wiesława Nizioł	Understanding p-adic etale cohomology of varieties 4 (Mercator lecture)
05.06.2025	Xiaoyu Zhang	t.b.a.
12.06.2025	Riccardo Tosi	t.b.a.
26.06.2025	–	Symposium Düsseldorf-Essen-Wuppertal
03.07.2025	ALGANT-Students	Presentation-try-out
10.07.2025	Sarah Zerbes (ETH Zurich)	t.b.a.
17.07.2024	Giulio Marazza	t.b.a.

Abstracts

Gautier Ponsinet: On a characterisation of perfectoid fields by Iwasawa theory

With a p-adic representation of the Galois group of a p-adic field are
associated the Bloch-Kato groups via p-adic Hodge theory. Iwasawa theory
motivates the study of these Bloch-Kato groups over infinite algebraic
extensions of the field of p-adic numbers.
Over perfectoid fields, several results provide a simple and useful
description of the Bloch-Kato groups.
In this talk, we will first present these results. We will then present
a reciprocal statement: the structure of the Bloch-Kato groups
associated with certain de Rham representations characterises the
algebraic extensions of the field of p-adic numbers whose completion is
a perfectoid field. In particular, we will recover, via a different
method, results by Coates and Greenberg for abelian varieties, and by
Bondarko for p-divisible groups.

Wiesława Nizioł: Understanding p-adic etale cohomology of varieties

This will be a gentle introduction to the geometric aspects of $p$-adic Hodge Theory. We will focus on $p$-adic etale cohomology of, mostly, algebraic varieties and the tools that allow us to understand it.

Johannes Sprang: Algebraicity and p-adic interpolation of critical Hecke L-values

Euler’s beautiful formula on the values of the Riemann zeta function at the positive even integers can be seen as the starting point of the investigation of special values of L-functions. In particular, Euler’s result shows that all critical zeta values are rational up to multiplication with a particular period, here the period is a power of 2πi. Conjecturally this is expected to hold for all critical L-values of motives. In this talk, I will explain a joint result with Guido Kings on the algebraicity of critical Hecke L-values up to explicit periods for totally imaginary fields. Afterwards, I will discuss recent work (partially in progress) on the construction of $p$-adic $L$-functions of such fields.