研究生教育创新计划GAP研讨班系列讲座之六十二

题目:   Fundamental groups of algebraic curves in positive characteristic

报告人：Jilong Tong (University of Bordeaux, France)
时间: 2015年11月6日, 周五 下午15:00-16:30  

地点：管研楼1611

摘要：Let $X$ be a proper connected smooth curve of genus at least two, defined over an algebraically closed field $K$.
The algebraic fundamental group $/pi_1(X)$ of $X$ is a profinite group associated with $X$, which classifies the
finite etale covers of $X$. When $K$ is of characteristic $0$ (for example when $K$ is the field of complex numbers),
the structure of $/pi_1(X)$ is uniquely determined by the genus of $X$. On the other hand, if $K$ is of positive
characteristic, the structure of $/pi_1(X)$ is much more involved. For example, A. Tamagawa proved that for an given
profinite group $/Gamma$, there exist only finitely many isomorphism classes of smooth connected projective curves  
of genus at least two defined over the algebraic closure of a finite field, whose fundamental group is isomorphic to
$/Gamma$. The aim of this talk is to explain some phenomenons in this direction.

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