Modular varieties and L-functions : in memoriam Jan Nekovář

28 mars 2024, 01:00 → 29 mars 2024, 12:30 Europe/Paris

Salle de conférences (IMB)

  

 SPEAKERS

David Burns (King's College London)

Kazim Büyükboduk (University College Dublin)

Christophe Cornut  (Institut de Mathématiques de Jussieu)           

Daniel Kriz (Institut de Mathématiques de Jussieu)    

Tony Scholl  (Cambridge)

Matteo Tamiozzo (Sorbonne Paris-Nord)

 

As part of the meeting,  Gulsin Onay offers a piano recital  on March 27th at 5 p.m. in the Salle des Actes of the University  (bat. A33). 

 

Organizers: Denis Benois and Mladen Dimitrov

 

 

 

 

jeudi 28 mars

09:15 Welcome coffee

1 Anthony J. Scholl, The plectic abelian polylogarithm

Abstract: I will discuss my joint work with Jan Nekovar, in which we constructed a refinement of the abelian Hodge-theoretic polylogarithm of Wildeshaus and Levin, and possible arithmetic applications.

11:00 Coffee break

2 Daniel Kriz, Motivic spaces and spectra and the plectic conjecture

Abstract. We formulate a motivic homotopy version of the plectic conjecture of Jan Nekovář and Tony Scholl by constructing a category of r-plectic motivic spaces and spectra, using the theory of Morel and Voevodsky. We show that this category satisfies the basic properties conjectured by Nekovář-Scholl in the case of pure Shimura data. This is joint work with Po Hu, Igor Kriz and Petr Somberg.

12:30 Lunch

3 David Burns, On recent advances in the theory of Euler systems

Abstract: We discuss work-in-progress with Dominik Bullach concerning the abstract theory of Euler and Kolyvagin systems for p-adic representations. We explain the motivation for work in this direction, the consequences of our current results for the study of special value conjectures and the key role played in their proofs by a foundational principle championed by Jan.

15:30 Coffee break

4 Kazim Büyükboduk, Chow--Heegner points and Artin formalism for triple product p-adic L-functions

Abstract: I will discuss the factorization of a certain triple product p-adic L-function whose interpolation range is empty. The relevant factorization statement reflects the Artin formalism for the underlying family of motives (that decompose as the sum of 2 motives of respective degrees 2 and 6). I will explain how this can be recast in terms of the interplay between cycles that are governed by the Gross--Zagier and (conjectural) Gross--Kudla--Schoen formulae for the relevant complex L-series.

The statement of this conjecture was conceived through calculations with Jan's interpretation of algebraic p-adic L-functions (as determinants of Selmer complexes). One unconditional evidence towards this conjecture is the verification of its algebraic counterpart that is formulated in terms of these.

19:30 Dinner at Café du Port

vendredi 29 mars

5 Christophe Cornut, Champs immobiliers

Résumé. Une proposition de géométrisation champêtre des immeubles de Bruhat-Tits.

11:00 Coffee break

6 Matteo Tamiozzo, Bipartite Kolyvagin systems and the structure of Selmer groups

Abstract. Bipartite Kolyvagin systems are incarnations of Jochnowitz congruences between special values of L-functions of congruent automorphic forms. In the case of Hilbert modular forms of parallel weight two, I will describe the connection between the p-parity conjecture and the non-triviality of such systems, and illustrate how they can be used to construct bases of Selmer groups modulo p. In the remaining time, I will discuss how the search for “higher Jochnowitz congruences” is related to the plectic conjectures.