Academic Year 2020/2021 - Number Theory Seminars

The Algebra and Number Theory group of the University of Luxembourg hosts three seminars.

Everyone is invited to attend! For more information, please contact Alexandre Maksoud, Andrea Conti or Gabor Wiese.


Luxembourg Number Theory Seminar

Date (Room) Speaker Title
13/10/2020, 14:00 (MSA 3.220)Gautier Ponsinet (Max Planck Institute for Mathematics)Universal norms of p-adic Galois representations and the Fargues-Fontaine curve
27/10/2020, 16:00 (online, MSA 3.220) Paul Pollack (University of Georgia) tba
03/11/2020, 14:00 (online, MSA 3.220) Nikita Karpenko (University of Alberta) An ultimate proof of Hoffmann-Totaro's conjecture
14/12/2020, all day (online) Luxembourg Number Theory Day 2020


Work in Progress Seminar

Date (Room) Speaker Title
29/09/2020, 14:00 (MSA 3.100) Alexandre Maksoud On Iwasawa theory and Bloch-Kato conjecture for Artin motives
06/10/2020, 13:30 (MSA 3.220) Daniel Berhanu Mamo Eisenstein series and newform theory
20/10/2020, 14:00 (MSA 3.220) Arturo Jaramillo/Xiaochuan Yang Selberg's theorem via Stein's method
27/10/2020, 14:00 (MSA 3.220) Sebastiano Tronto tba
10/11/2020, 14:00 (MSA 3.220) Arturo Jaramillo tba
17/11/2020, 14:00 (MSA 3.220) Andrea Conti tba
24/11/2020, 14:00 (MSA 3.220) Antonella Perucca Kummer theory for 1-dimensional tori defined over number fields


Working Group: Adic spaces (Winter semester 2020)

You can find here a tentative schedule.

Date (Room) Speaker Title
29/09/2020, 10:30 (MSA 3.100) Andrea Conti Introduction
06/10/2020, 10:30 (MSA 3.220) Bryan Advocaat Valuations
13/10/2020, 10:30 (MSA 3.220) Alexandre Maksoud Spectral and sober spaces
20/10/2020, 10:30 (MSA 3.220) Daniel Berhanu Mamo Valuation spectra
27/10/2020, 10:30 (MSA 3.220) ? Non-archimedean rings
03/11/2020, 10:30 (MSA 3.190) ? f-adic rings and Tate rings
10/11/2020, 10:30 (MSA 3.220) ? Adic spectra of affinoid rings, I
17/11/2020, 10:30 (MSA 3.220) ? Adic spectra of affinoid rings, II
24/11/2020, 10:30 (MSA 3.220) ? Adic spaces, I
01/12/2020, 10:30 (MSA 3.220) ? Adic spaces, II
08/12/2020, 10:30 (MSA 3.220) ? From rigid analytic spaces and formal schemes to adic spaces


Collection of abstracts

Alexandre Maksoud (uni.lu) On Iwasawa theory and Bloch-Kato conjecture for Artin motives

Inspired by the works of Perrin-Riou and of Benois we formulate a new cyclotomic Iwasawa Main Conjecture (IMC) for Artin motives, as well as an Exceptional Zeros Conjecture in this context. When the Artin representation is monomial, we show that our conjectures follow from the higher rank cyclotomic IMC recently introduced by Burns, Kurihara and Sano, together with the Iwasawa-theoretic Mazur-Rubin-Sano conjecture. We highlight some potential applications to a better understanding of special values of Artin L-functions at $s=0$, and to a conjecture on iterated p-adic integrals of Darmon-Lauder-Rotger.

Daniel Berhanu Mamo (uni.lu) Eisenstein series and newform theory

We set up a variant of strong multiplicity one theorems for Katz modular forms which admit a reducible mod $p$ Galois representation. An example that illustrates the main theorem will be presented.

Gautier Ponsinet Universal norms of $p$-adic Galois representations and the Fargues-Fontaine curve

In 1996, Coates and Greenberg computed explicitly the module of universal norms for abelian varieties in perfectoid field extensions. The computation of this module is essential to Iwasawa theory, notably to prove "control theorems" for Selmer groups generalising Mazur's foundational work on the Iwasawa theory of abelian varieties over $\mathbb{Z}_p$-extensions. Coates and Greenberg then raised the natural question on possible generalisations of their result to general motives. In this talk, I will present a new approach to this question relying on the classification of vector bundles over the Fargues-Fontaine curve, which enables to answer Coates and Greenberg's question affirmatively in new cases.

Arturo Jaramillo and Xiaochuan Yang (uni.lu) Selberg's theorem via Stein's method

Click here for the abstract.

Nikita Karpenko (University of Alberta) An ultimate proof of Hoffmann-Totaro's conjecture

We prove the last open case of the conjecture on the possible values of the first isotropy index of an anisotropic quadratic form over a field. It was initially stated by Detlev Hoffmann for fields of characteristic not 2 and then extended to arbitrary characteristic by Burt Totaro. The initial statement was proven by the speaker in 2002. In characteristic 2, the case of a totally singular quadratic form was done by Stephen Scully in 2015 and the nonsingular case by Eric Primozic in early 2019.

Antonella Perucca (uni.lu) Kummer theory for 1-dimensional tori defined over number fields

Classical Kummer theory concerns the study of cyclotomic-Kummer extensions, which can be interpreted as torsion and division fields for the multiplicative group. It is natural to address the same problems for general 1-dimensional tori, thus covering also the non-split case. In this talk I will explain how to compute the degree of division fields for non-split 1-dimensional tori defined over a number field. The strategy is reducing to the case of the multiplicative group, which amounts to understanding whether the splitting field of the torus is contained or not in the given division field. If time permits we will also address similar questions for products of 1-dimensional tori.


Last modification: 14 October 2020.