STAGE Seminar

Friday, October 12, 2018 at 10:00am to 12:00pm

2-139

Siyan Daniel Li

A Finitude Theorem for Galois Representations

We will first use properties of étale cohomology to motivate the study of Galois representations. Next, we will prove a result of Faltings saying that, given some natural constraints, there are finitely many such representations. The proof relies on Minkowski's bound and Chebotarev's density theorem. Finally, time permitting, we will explain how Faltings used this result, along with Tate's conjecture for abelian varieties, to prove Shafarevich's conjecture (which in turn implies Mordell's conjecture).

 

Event Type

Conferences/Seminars/Lectures

Events By Interest

Academic

Events By Audience

Public

Tags

harmonjo, stage_sem

Website

http://math.mit.edu/nt/index_stage

Department
Department of Mathematics
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