報告人：唐詩昂 猶他大學(xué) 在讀博士
報告時間：2017.5.23 周二 16:00—17:00
地點：X2536
報告題目：Algebraic monodromy group and Galois deformation theory
報告摘要：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.
