Joint Number Theory Seminars at Beijing

Saturday, July 21, 2007

Shouwu Zhang: Rational Points on Curves

丘镇英学术讲座
晨兴数学中心 主办
报告人: Prof. Shouwu Zhang
(University of Columbia, USA)
系列报告标题:
Rational Points on Curves
系列报告摘要:The structure of rational solutions to a polynomial equation depends on the structure of corresponding algebraic variety. In case of a curve of genus zero, the problem of find all solutions can be completely solved using Hasse-Minkowski principle is conjectured to be finite; and the set of rational points is a finitely generated group by the Mordell-Weil theorem if it not empty. In case of genus two or bigger, the set of solutions is finite by Faltings theorem.
A major unsolved problem today is the effectivity of solutions for curves of genus one or bigger。 For elliptic curves, one has the Birch and Swinner-Dyer(BSD) conjecture which related the
Mordell-Weil group and the central values of L-Series arsing from counting rational points over finite fields. For curves of genus two of bigger, one has the ABC conjecture and its refinements providing some effective bounds for curves. In function field case, these conjectures are consequences of Bogomolov-Miyaoka-Yau.
报告时间:2007年7月26日 10:00am
2007年7月31日 10:00am
2007年8月 3日10:00am
报告地点:晨兴数学中心110报告厅

overview

BSD
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