Winter Term 2013 - Working Group on Number Theory

We meet in the lecture room of the library in the G-building.

We regularly hold two seminars:

Number Theory Seminar/Work in progress

Everyone is invited to attend! For more information, please contact Gabor Wiese.

Date Speaker Title
09/10/2013, 16:15 Agnès David On the irreducibility of Galois representations attached to elliptic curves
23/10/2013, 16:15 Hwajong Yoo Index of Eisenstein ideals and multiplicity one
30/10/2013, 16:15 Mladen Dimitrov (Lille)A finiteness result on the rational points on a class of Picard modular surfaces
06/11/2013, 16:15 Hwajong Yoo Modularity of reducible Galois representations
20/11/2013, 16:15 Allorbi-session
27/11/2013, 16:15 Xavier Caruso (Rennes)Computation of some Galois deformation rings in the Breuil-Mézard settings
11/12/2013, 16:15 Tommaso Centeleghe (Heidelberg)On abelian varieties over finite fields


Xavier Caruso: Computation of some Galois deformation rings in the Breuil-Mézard settings

Let p be a prime number \geq 5 and F be an unramified extension of \Q_p. Consider in addition \bar\rho a representation over \bar\F_p of the absolute Galois group of F. To these data, one can associate a ring R(\bar\rho) which parameters deformations of \rho\bar over arbitrary complete local noetherian \bar\Z_p-algebras having residue field \bar\F_p. Breuil-Mézard conjecture predicts the geometry of the special fibres of some quotients R(v,t,\bar\rho) of R(\bar\rho), where v and t are two new parameters coming from p-adic Hodge theory. In this talk, I will present a work in progress with David and Mézard whose aim is to compute explicitely certain rings R(v,t,\bar\rho) and check for them the Breuil-Mézard conjecture.

Tommaso Centeleghe: On abelian varieties over finite fields

Thanks to an old result of Deligne, the category of ordinary abelian varieties over a fixed finite field can be described in terms of finite free Z-modules equipped with a linear operator F (playing the role of Frobenius) satisfying certain axioms. In a recent joint work with Jakob Stix, we prove a similar result for the full subcategory of all abelian varieties over the prime field supported on a finite set of non-real Weil numbers, thereby obtaining a description of non-ordinary isogeny classes in Deligne's spirit. In the talk I will describe the method we use.

Last modification: 29 November 2013.