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几何拓扑讨论班学术报告

来源:  作者:数学中心     日期:2017/5/16 0:00:00   点击数:1418  

报告人:唐诗昂 犹他大学 在读博士

报告时间:2017.5.23 周二 16:0017:00

地点:X2536

 

报告题目:Algebraic monodromy group and Galois deformation theory

 

报告摘要:An algebraic monodromy group is a reductive algebraic group that arises as the Zariski closure of the image of certain p-adic Galois representation. Recent advances in potential automorphy theorems allows one to prove that certain algebraic groups arise in this way and the Galois representation is geometric in the sense of Fontaine-Mazur. They provide evidences for generalized Serre-type conjectures. But potential automorphy techniques are currently quite limited outside of classical groups. The theory of Galois deformation allows us to investigate cases that cannot currently be settled using potential automorphy. It is a very subtle question classifying reductive groups that arise from geometric p-adic Galois representations. For instance, GL_2 is a monodromy group coming from elliptic curves but there are good reasons for SL_2 to not arise in similar ways! Using Galois deformation theory, we answer a weaker form of this question by showing that most of the reductive groups do come from (not necessarily geometric) p-adic Galois representations.