Séminaire Théorie des Nombres

Responsables : Eric Balandraud, Andrea Fanelli.

Le 24 mars 2023 à 14:00

Salle de Conférences

Dino Lorenzini (Georgia)

Torsion and Tamagawa numbers

Associated with an abelian variety A/K over a number field K is a finite set of integers greater than 1 called the local Tamagawa numbers of A/K. Assuming that the abelian variety A/K has a K-rational torsion point of prime order N, we can ask whether it is possible for none of the local Tamagawa numbers to be divisible by N. The ratio (product of the Tamagawa numbers)/|Torsion in E(K)| appears in the conjectural leading term of the L-function of A in the Birch and Swinnerton-Dyer conjecture, and we are thus interested in understanding whether there are oftencancellation in this ratio.We will present some finiteness results on this question in the case of elliptic curves. More precisely, let d>0 be an integer, and assume that there exist infinitely fields K/Q of degree d with an elliptic curve E/K having a K-rational point of order N. We will show that for certain such pairs (d,N), there are only finitely many fields K/Q of degree d such that there exists an elliptic curve E/K having a K-rational point of order Nand none of the local Tamagawa numbers are divisible by N. The lists of known exceptions are surprisingly small when d is at most 7.

Le 31 mars 2023 à 14:00

Salle de Conférences

Quentin Gazda (École Polytechnique)

À préciser

À préciser

Le 7 avril 2023 à 14:00

Salle de Conférences

Adel Betina (Copenhague)

À préciser

À préciser

Le 14 avril 2023 à 14:00

Salle de Conférences

Ratko Darda (Bâle)

À préciser

À préciser

Le 28 avril 2023 à 14:00

Salle de Conférences

Francesco Lemma (IMJ Paris)

À préciser

À préciser

Le 5 mai 2023 à 14:00

Salle de Conférences

Séverin Philip (Kyoto)

À préciser

À préciser

Le 26 mai 2023 à 14:00

Salle de Conférences

Luca Tasin (Milan)

À préciser

À préciser

Les séminaires depuis 2013

Séminaire Théorie des Nombres

Institut de Mathématiques de Bordeaux UMR 5251