[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (23/10/2014, Alastair Irving, Jennifer Park)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Wed Oct 22 10:25:29 EDT 2014


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 23 octobre 2014 / Thursday, October 23, 2014

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

CONFERENCIER(S) / SPEAKER(S) :
Alastair Irving (Université de Montréal)

TITRE / TITLE :
Cubic polynomials represented by norm forms 

LIEU / PLACE :
CRM, Université de Montréal, Pav. André Aisenstadt, 2920 chemin de la Tour, salle 6214

RESUME / ABSTRACT :
We will discuss how analytic techniques, specifically sieves, can be used to study a problem in arithmetic geometry. For norm forms $N$ from certain number fields and irreducible cubic polynomials $f$, we will establish the Hasse principle for the variety defined by $$f(t)=N(x_1,\ldots,x_k).$$


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DATE :
Le jeudi 23 octobre 2014 / Thursday, October 23, 2014

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

CONFERENCIER(S) / SPEAKER(S) :
Jennifer Park (McGill University)

TITRE / TITLE :
Effective Chabauty for symmetric powers of curves.

LIEU / PLACE :
CRM, Université de Montréal, Pav. André Aisenstadt, 2920 chemin de la Tour, salle 6214

RESUME / ABSTRACT :
Faltings' theorem states that curves of genus g> 1 have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound on the number of rational points, but this bound is too large to be used in any reasonable sense. In 1985, Coleman showed that Chabauty's method, which works when the Mordell-Weil rank of the Jacobian of the curve is smaller than g, can be used to give a good effective bound on the number of rational points of curves of genus g > 1. We draw ideas from nonarchimedean geometry and tropical geometry to show that we can also give an effective bound on the number of rational points outside of the special set of the d-th symmetric power of X, where X is a curve of genus g > d, when the Mordell-Weil rank of the Jacobian of the curve is at most g-d.


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Responsable(s) :
Henri Darmon (darmon at math.mcgill.ca)
Andrew Granville (andrew at dms.umontreal.ca)
Dimitris Koukoulopoulos (koukoulo at CRM.UMontreal.CA)
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http://www.dms.umontreal.ca/~qvnts/QVNTSinfo.html


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