## 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 | All | orbi-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 |

#### Abstracts

##### 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.