Arithmetica Transalpina

Brig, May 17, 2024

This is the second meeting of the Arithmetica Transalpina, a joint Number Theory seminar between ETH Zürich, FernUni Schweiz and the Universities of Milan, Padova and Genova.

Location: The meeting will take place in the UniDistance Suisse, Schinerstrasse 18, 3900 Brig. The talks will start at 11:30am, with refreshments being available from 11am. In the evening, there will be a reception from 6:30 - 7:30pm, and conference dinner starting at 8pm.

Organizers: Fabrizio Andreatta (Milan) – David Loeffler (FernUni Schweiz) – Matteo Longo (Padova)  – Stefano Vigni (Genova)  – Sarah Zerbes (ETH Zürich). 


  • Massimo Bertolini (Essen)
  • Harald Grobner (Vienna)
  • Yukako Kezuka (Jussieu)
  • Chris Lazda (Exeter)


11.00–11.30 Welcome and refreshments
11.30–12.30 Lazda, An overconvergent Riemann-Hilbert correspondence
According to a philosophy of Grothendieck, every good cohomology theory should have a six functor formalism. Arithmetic D-modules were introduced by Berthelot to provide the theory of rigid cohomology with exactly such a formalism. However, it is not clear that cohomology groups computed via the theory of arithmetic D-modules coincide with the analogous rigid cohomology groups. In this talk I will describe an overconvergent Riemann-Hilbert correspondence that can be used to settle this question.
12.30–13.45 Lunch
13.45–14.45 Kezuka, Non-commutative Iwasawa theory of abelian varieties
We consider an abelian variety A defined over various base fields F, and discuss its arithmetic over the cyclotomic Z_p-extension and more general p-adic Lie extensions. After reviewing some known results over number fields, we shift our focus to the case of global function fields. In this context, we compare the arithmetic of A over different p-adic Lie extensions without assuming the finiteness of the Selmer group of A over the base field F.
15.00–16.00 Bertolini, The anticyclotomic main conjectures
I will report on a recently completed work in collaboration with Matteo Longo and Rodolfo Venerucci on the proof on the anticyclotomic main conjectures of Iwasawa theory for elliptic curves. Our work covers the ordinary and supersingular case, as well as the definite and indefinite setting.
16.15–17.15 Grobner, On the existence of CM-motives and Deligne’s conjecture for motivic L-functions
A celebrated conjecture of Deligne states that every critical value of a motivic L-functions is a certain algebraic multiple of a geometrically defined period. Whereas a conjecture of Clozel predicts a correspondence between irreducible motives and algebraic cuspidal automorphic representations of GL(n). In this talk we will describe our (party conditional) proof of both conjectures in the case, when the underlying number field is of CM-type and the cuspidal automorphic representations in sight are suitable functorial lifts from unitary groups. (This is joint work with M. Harris and J. Lin.)
17.30–18.30 Drinks reception at Alte Simplonstrasse 20
18.30– Dinner at Restaurant Schlosskeller


The meeting is funded by ETH Zürich and by the ERC Consolidator Grant ``Shimura varieties and the Birch--Swinnerton-Dyer conjecture''.