[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (28/01/2016, Eyal Goren, Will Chen)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Tue Jan 26 15:25:16 EST 2016


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 28 janvier 2016 / Thursday, January 28, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Eyal Goren (McGill University)

TITRE / TITLE :
Picard modular surfaces in positive characteristic

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
The theory of modular curves, their integral models and modular forms on them is well-developed, and had been used in many spectacular applications. I will recall some of the features that are relevant to my talk. 

Motivated by the state of affairs for curves, we have been studying unitary Shimura varieties in positive characteristic and, in particular, the Picard modular surfaces that are associated to a unitary group of signature (2,1). These are moduli spaces for abelian threefolds equipped with an action of an imaginary quadratic field. I will explain what we currently know about their geometry modulo a prime p (building on work by Bellaiche, Vollaard, Bultel-Wedhorn and borrowing ideas from G. Boxer and the theory of modular curves). To the extent time allows, I will discuss Hecke correspondences at p and the rather complicated picture we face. 

This is joint work with E. De Shalit (Hebrew University).


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DATE :
Le jeudi 28 janvier 2016 / Thursday, January 28, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Will Chen (Penn State University)

TITRE / TITLE :
Moduli Interpretations for Noncongruence Modular Curves

LIEU / PLACE :
Concordia University, Library Building, 9th floor

RESUME / ABSTRACT :
Quotients of the upper half plane H by congruence subgroups of SL(2,Z) are well known to be moduli spaces parametrizing elliptic curves equipped with "abelian" level structures. In my talk I will consider Teichmuller level structures on elliptic curves attached to finite groups G, and show that when G is sufficiently nonabelian, the resulting moduli spaces are noncongruence modular curves (quotients of H by noncongruence subgroups of SL(2,Z)). When G is abelian, we recover standard congruence level structures. I will also discuss connections with the inverse Galois problem, as well as the unbounded denominators conjecture for noncongruence modular forms.


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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


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