[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (25/01/2018, Valentin Hernandez, Julia Brandes)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Tue Jan 23 09:46:54 EST 2018


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 25 janvier 2018 / Thursday, January 25, 2018

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

CONFERENCIER(S) / SPEAKER(S) :
Valentin Hernandez (Barcelona)

TITRE / TITLE :
Families of Picard modular forms and an application to the Bloch-Kato conjecture

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
About 15 years ago, Bellaïche and Chenevier showed how to prove a particular case of the Bloch-Kato conjecture for some Hecke characters of a quadratic imaginary field, using families of automorphic forms for a compact at infinity unitary group in 3 variables U(3), and a endoscopic result of Rogawski.
The aforementioned endoscopic transfer associate to such a Hecke character of sign -1 at the center of the functional equation an algebraic automorphic representation of U(3). When the sign is +1, Rogawski also associate to these characters an algebraic automorphic representation of U(2,1), a three variables unitary group, split at infini
In these talk, we will explain how to construct $p$-adic families of automorphic forms for U(2,1), in particular when p is inert, and thus when the (p-)ordinary locus is empty in the Picard modular surface. Then, we will explain how to use these families to extend the construction of Bellaïche and Chenevier to a character of sign +1.

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DATE :
Le jeudi 25 janvier 2018 / Thursday, January 25, 2018

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

CONFERENCIER(S) / SPEAKER(S) :
Julia Brandes (Waterloo/Chalmers)

TITRE / TITLE :
Linear spaces on cubic hypersurfaces

LIEU / PLACE :
Concordia University, Library Building, 9th floor, room LB 921-4

RESUME / ABSTRACT :
One of the most intensely studied question in the intersection of analytic number theory and algebraic geometry concerns the existence and distribution of rational points on cubic hypersurfaces, but the analogous question regarding lines or higher-dimensional linear spaces is far less understood. In this talk, we will show that every smooth cubic hypersurface of projective dimension at least 29 contains a rational line, superseding earlier bounds due to Dietmann and Wooley. We will then discuss some of the consequences and generalisations of this result. This is joint work with Rainer Dietmann.

Responsable(s) :
Henri Darmon (Henri.darmon at mcgill.ca)
Adrian Iovita (adrian.iovita at concordia.ca)
Maksym Radziwill (maksym.radziwill at gmail.com)
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