[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (08/02/2018, Lucile Devin Evangelia Gazaki)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Mon Feb 5 10:02:51 EST 2018


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 8 février 2018 / Thursday, February 8, 2018

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

CONFERENCIER(S) / SPEAKER(S) :
Lucile Devin (University of Ottawa)

TITRE / TITLE :
Chebyshev's bias for products of irreducible polynomials 

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
Following the work of B. Cha, we adapt new results related to the Chebyshev's bias questions in the setting of polynomial rings. For any finite field F, and for any positive integer k, we study the distribution of products of k irreducible polynomials with coefficients in F in congruence classes. We obtain unconditional results for the existence of the bias. We put the emphasis on the difference from the original setting due to unexpected zeros. Joint with X. Meng.


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DATE :
Le jeudi 8 février 2018 / Thursday, February 8, 2018

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

CONFERENCIER(S) / SPEAKER(S) :
Evangelia Gazaki (University of Michigan)

TITRE / TITLE :
Zero cycles on products of elliptic curves over Ap-Adic field

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

RESUME / ABSTRACT :
The theory of algebraic cycles relates to some of the most fascinating conjecturesin arithmetic geometry, like the Tate conjecture and the Bloch-Beilinson conjectures.In this talk I will focus on the case of zero cycles, namely on the group CH0(X) of zerocycles modulo rational equivalence on a smooth projective variety X over a field K. WhenX has a K-rational point, there is an Abel-Jacobi map,CH0(X)degree=0 −→ AX(K),to an abelian variety, AX. When the base field K is a number field, the Bloch-Beilinsonconjectures predict that the abelian group CH0(X) is finitely generated, while the kernel ofthe Abel-Jacobi map is expected to be torsion. When K is a finite extension of the p-adicfield Qp, it is a conjecture of Colliot-Th´el`ene that the kernel is the direct sum of a finitegroup and a divisible group.In this talk I will present some very recent work, joint with Isabel Leal. In this work,we prove the aforementioned conjecture of Colliot-Th´el`ene for a product of elliptic curvesover a p-adic field under some assumptions on the reduction type, extending previous workof Raskind and Spiess. Most importantly, we obtain significant new information on thecycle map to ´etale cohomology, allowing us to obtain some initial evidence towards globalquestions.


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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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