On the local arithmetic of hyperelliptic curves

：刘青（法国波尔多大学）
：2025-10-29 10:00
：海韵园实验楼S204

报告人：刘青（法国波尔多大学）

时  间：2025年10月29日10:00

地  点：海韵园实验楼S204

内容摘要:

Birch and Swinnerton-Dyer's conjecture predicts a precise relation between the L-function of an elliptic curve over the rational numbers and some arithmetic invariants of the elliptic curve. This conjecture has a generalized version for abelian varieties over number fields. For abelian varieties which are Jacobians of curves, some of the corresponding invariants can be read from the curves. In this talk I will explain how this is done "concretely". For hyperelliptic curves, there are even computer program determining these invariants away from the prime 2. I will describe an algorithm for the prime 2.

个人简介：

刘青，法国波尔多大学教授。2013年-2022年期间曾兼任厦门大学讲座教授。1987年博士毕业于法国波尔多大学，研究领域为代数几何与算术几何，著有一本颇有影响的教材《Algebraic Geometry and Arithmetic Curves》，在Inventiones mathematicae, Duke Mathematical Journal, Compositio Mathematica, Journal of Algebraic Geometry, Mathematische Annalen等重要期刊上发表多篇文章。曾是Journal de Théorie des Nombres de Bordeaux的编委。

 

联系人：刘文飞