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