[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (24/03/2016, Ashay Burungale, Shaunak Deo, Lucio Guerberoff)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Wed Mar 23 10:05:50 EDT 2016

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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 24 mars 2016 / Thursday, March 24, 2016

HEURE / TIME :
10 h 30 - 12 h / 10:30 a.m. - 12:00 p.m.

CONFERENCIER(S) / SPEAKER(S) :
Ashay Burungale (UCLA)

TITRE / TITLE :
Horizontal non-triviality of Heegner points and central L-values

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
Let F be a totally real field and A a modular abelian variety over F.
Let K/F be a CM quadratic extension. Let \chi be a class group character over K
such that generalised Heegner hypothesis holds for the pair (A,\chi).
We sketch our recent result showing that the number of class group characters \chi with bounded ramification such that $L'(1, A, \chi) \neq 0$ increases with the absolute value of the discriminant of K. We also discuss a rank zero situation. For both situations, the approach is geometric relying on the Zariski density of CM points in self-products of a quaternionic Shimura variety (joint with H. Hida and Y. Tian).

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DATE :
Le jeudi 24 mars 2016 / Thursday, March 24, 2016

HEURE / TIME :
14 h - 15 h 30 / 2:00 p.m. - 3:30 p.m.

CONFERENCIER(S) / SPEAKER(S) :
Shaunak Deo (Braindeis University)

TITRE / TITLE :
Hilbert modular eigenvariety at classical points of parallel weight one

LIEU / PLACE :
Concordia University, Library Building, 9th floor, Salle/Room 921-04

RESUME / ABSTRACT :
We sketch our recent results about the geometry of the p-adic eigenvariety constructed by Andreatta-Iovita-Pilloni, which interpolates Hilbert modular eigenforms over a totally real field F, at classical, regular points of parallel weight one with dihedral projective image. To prove these results, we assume the Leopoldt conjecture for certain quadratic extensions of F in some cases and the p-adic Schanuel conjecture in some cases. In some cases, we get the results unconditionally. The key ingredient in our proof is calculation of the dimension of the tangent spaces of some Galois deformation problems.

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DATE :
Le jeudi 24 mars 2016 / Thursday, March 24, 2016

HEURE / TIME :
16 h - 17 h / 4:00 p.m. - 5:00 p.m.

CONFERENCIER(S) / SPEAKER(S) :
Lucio Guerberoff (University College London)

TITRE / TITLE :
Period relations for automorphic forms on unitary groups and critical values of L-functions

LIEU / PLACE :
Concordia University, Library Building, 9th floor, Salle/Room 921-04

RESUME / ABSTRACT :
In this talk I will explain some results relating critical values of L-functions of cohomological automorphic representations of unitary groups over CM fields and periods. I will explain a formula expressing the critical values in terms of Petersson norms of holomorphic forms, and we explain the link with Deligne's conjecture, which predicts that these have a factorization in terms of quadratic periods, depending on the signature of the unitary group.

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Responsable(s) :
Henri Darmon (darmon at math.mcgill.ca)
Andrew Granville (andrew at dms.umontreal.ca)
Dimitris Koukoulopoulos (koukoulo at dms.umontreal.ca)
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http://www.dms.umontreal.ca/~qvnts/QVNTSinfo.html