[Liste-CICMA] ( À LAVAL ) - SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (20/05/2015, Daniel Delbourgo, Carl Wang Erickson)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Mon May 11 10:20:07 EDT 2015


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le mercredi 20 mai 2015 / Wednesday, May 20, 2015

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

CONFERENCIER(S) / SPEAKER(S) :
Daniel Delbourgo (Waikato University)

TITRE / TITLE :
Non-commutative Iwasawa theory of elliptic curves in 3-d

LIEU / PLACE :
Université Laval, 3840, Pavillon Alexandre-Vachon

RESUME / ABSTRACT :
We discuss some p-power congruences between L-values of
elliptic curves, and explain how they arise from the "shape" of a big
Selmer group. We then focus on p-adic Lie extensions of dimension 3,
and show how one can obtain lower bounds on the Selmer rank up the
tower. This is joint work with Lloyd Peters and Antonio Lei.


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DATE :
Le mercredi 20 mai 2015 / Wednesday, May 20, 2015

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

CONFERENCIER(S) / SPEAKER(S) :
Carl Wang Erickson (Brandeis  University)

TITRE / TITLE :
Pseudo-modularity on the ordinary eigencurve

LIEU / PLACE :
Université Laval, 3840, Pavillon Alexandre-Vachon

RESUME / ABSTRACT :
Hida theory says that any ordinary eigenform lies in a family of ordinary eigenforms with p-adically varying coefficients and weight. Sometimes, these families collide. We will discuss joint work with Preston Wake in which we investigate the collisions between the Eisenstein family and cuspidal families, showing that if we assume a mild condition on class groups, the collision is a plane singularity. We also determine when it is a simple normal crossing and draw consequences in Iwasawa theory, namely, new cases of Sharifi's conjecture. Time permitting, we will discuss the technique, which is to construct a deformation ring for ordinary Galois pseudorepresentations and compare this ring with the local ring on the eigencurve; in fact, we show they are isomorphic, a "pseudo-modularity" theorem. 


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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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