Vendredi 2 Juin
Heure: 
09:45  10:30 
Lieu: 
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13 
Résumé: 
Géométrie Arithmétique et Motivique  On the padic interpolation of Asai Lvalues  
Description: 
PakHin LeeOne theme of the relative Langlands program is that period integrals of an automorphic representation of G over a subgroup H often detect functorial transfer from some other group G'; moreover, such period integrals often compute special Lvalues. It is natural to expect padic Lfunctions interpolating these period integrals as the automorphic representation varies in padic families, which should encode geometric information about the eigenvariety of G. In this talk, we consider the FlickerRallis periods, for which G =GL_n(K) and H = GL_n(Q) for an imaginary quadratic field K and outline the construction of a padic Lfunction on the eigenvariety of G interpolating certain noncritical Asai Lvalues. We discuss the case n=2 in some detail before moving on to general n, which is work in progress with Daniel Barrera Salazar and Chris Williams. 
Heure: 
11:00  12:00 
Lieu: 
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13 
Résumé: 
Géométrie Arithmétique et Motivique  Galois representation of partially classical Hilbert modular forms  
Description: 
ChiYun HsuLet F be a totally real field. A Hilbert modular form is a section of a modular sheaf, defined over the whole Hilbert modular variety associated to F, while a padic overconvergent form is defined only over a strict neighborhood of the ordinary locus. For each subset I of the primes of F above p, one has the intermediate notion of Iclassical Hilbert modular forms by replacing ordinary by Iordinary. Given an overconvergent Hecke eigenform f, we have the associated Galois representation rho, which is wellknown to be de Rham at p when f is classical. We prove that rho is Ide Rham when f is Iclassical. The idea is to padically deform f in the weight direction of the complement of I, and knowing that classical points are dense and Ide Rham points are closed when the IHodge Tate weights are fixed. 

