[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (27/10/2016, V. Dokschitser and C. Maistret, A. Morgan and V. Dokschitser)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Mon Oct 24 09:39:08 EDT 2016


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 27 octobre 2016 / Thursday, October 27, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Vladimir Dokschitser and Celine Maistret (Warwick)

TITRE / TITLE :
Arithmetic of hyperelliptic curves over local fields

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
Let C:y^2 = f(x) be a hyperelliptic curve over a local field K of odd residue characteristic. We show how several arithmetic invariants of the curve and its Jacobian, including its potential stable reduction, Galois representation and (in the semistable case) Tamagawa numbers, can be simply extracted from combinatorial data coming from the roots of f(x). As an application, we give an explicit construction of abelian varieties A/Q with Gal(Q(A[p])/Q) = GSp(2n;p) for all odd primes p.

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DATE :
Le jeudi 27 octobre 2016 / Thursday, October 27, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Adam Morgan and Vladimir Dokchitser (Warwick)

TITRE / TITLE :
Parity of ranks of abelian varieties

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

RESUME / ABSTRACT :
Let K be a number field and A/K an abelian variety. A basic consequence of the Birch and Swinnerton-Dyer conjecture is the parity conjecture: the sign of the functional equation of the L-series determines the parity of the rank of A/K. Under suitable local constraints and finiteness of the Shafarevich-Tate group, we prove the parity conjecture in two new cases. Firstly for principally polarized abelian surfaces and secondly, over quadratic extensions of the base field, for Jacobians of hyperelliptic curves. We also prove analogous unconditional results for Selmer groups.


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Responsable(s) :
Henri Darmon (darmon at math.mcgill.ca)
Eyal Z. Goren (eyal.goren at mcgill.ca)
Chantal David (cdavid at mathstat.concordia.ca)
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