We meet in the lecture room of the library in the G-building.
We regularly hold two seminars:
Everyone is invited to attend! For more information, please contact Gabor Wiese.
|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|
|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|
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.
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.