number theory seminar today
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William Stein
Nov 8, 2012, 9:14:13 AM11/8/12
to ntuw, 581...@googlegroups.com, Alyson Deines, Benjamin Lundell, Ralph Greenberg
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
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
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