number theory seminar this Thursday, Nov 8

[William Stein]

Hi,

This is the announcement for the number theory seminar this week.

Coordinates: Nov 8 at 10:30am in Padelford C401

Speaker: Alyson Deines (University of Washington)

Title: More on Level Lowering: Examining Ribet's short exact sequence.

Abstract:

On the way to level lowering,  Ribet uses a short exact sequence of character groups relating modular and Shimura curves.   In particular,  let $L$ be the character group of the modular curve $X_0(pqM)_{\mathbb{F}_q}$,  $X$ the character group of the modular curve $X_0(qM)_{\mathbb{F}_q}$, and $Z $ the character group of the Shimura curve $X_0^{pq}(M)$.   Finally, let $Y$ be the kernel of $\delta : L \rightarrow X \oplus X$.   Then by showing $Y \cong Z$ we have Ribet's short exact sequence:

     $$0 \rightarrow Z \rightarrow L \rightarrow X \oplus X \rightarrow 0.$$  

In this talk I will explain the isomorphism $Y \cong Z$.

--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org