| Thu, Feb 23, 2023
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Number Theory Seminar
3:00 PM
MSCS 514 | | Local Data of Isogenous Elliptic Curves
Bella Tobin, Oregon State University
Host: Paul Fili
| | | Abstract: Given a minimal proper regular model of an elliptic curve
$E$ for a prime $p$, we can
compute the local data at $p$. This includes the special fiber of the
minimal model (i.e., N\'{e}ron
type), the conductor exponent of $E$ at $p$, and the local
Tamagawa number at $p$. While in many cases it is known how local data
varies over isogeny, it is unknown how the N\'{e}ron type and Tamagawa
number change for elliptic curves with wild ramification under 2- or
3- isogeny. Our goal is to determine how the N\'{e}ron types and
Tamagawa numbers of isogenous elliptic curves change in this latter
case. To answer this question, we examine how local data of rational
elliptic curves change under quadratic twists. This is an ongoing
project with Barrios, Roy, Sahajpal, Tallana, and Wiersema. |
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