Number Theory Seminar reminder -- "Szpiro's Conjecture and Level Lowering"

[William Stein]

Hello,

This is a reminder that Soroosh Yazdani (who was a Berkeley grad student
of Ken Ribet and now works at McMaster University) will be speaking in
our Number Theory Seminar tomorrow (Tuesday, November 27) at 4:10pm.
The title and abstract are below.

Title: Szpiro's Conjecture and Level Lowering
Speaker: Soroosh Yazdani (McMaster University)
Location: Padelford C401 at 4:10pm on Tuesday, November 27, 2007
Abstract:
Let $E/\QQ$ be an elliptic curve over the rationals. Two invariants
attached to such elliptic curves are the minimal discriminant of $E$,
$\Delta_E$, and the conductor of $E$, $N_E$. One knows that $N_E |
\Delta_E$.
Szpiro's conjecture states that for any $\epsilon>0$ there exists
constant $C_\epsilon > 0$ such that for any elliptic curve $E/\QQ$ we
have
\[ |\Delta_E| < C_\epsilon (N_E)^{6+\epsilon}. \]
In this talk, I will look at a similar conjecture that is implied by
Szpiro. Specifically, if N_E=Mp with p large, then one expects
$v_p(\Delta_E) \leq 6$. I will show how general level lowering results
on modular forms can prove this conjecture for small values of $M$.

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