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Sporadic points on modular curves (Ozlem Ejder, Colorado State University)

October 15 @ 12:15 pm - 1:10 pm

A classic and fundamental result in number theory is due to Mordell who proved that the set of points on an elliptic curve defined over a number field forms a finitely generated abelian group; in particular, it has a finite torsion subgroup. An essential tool to study elliptic curves is the modular curves which are moduli spaces for elliptic curves with an additional structure.  In particular, $X_1(n)$ classifies the elliptic curves with a point of order of $n$.  Motivated by the classification of torsion problems, we study the sporadic points on the curve $X_1(n)$, that is, the closed points on $X_1(n)$ such that there are at most finitely many points of degree at most $\deg(x)$. In this talk, we will discuss the finiteness of sporadic points. This is joint with A. Bourdon, Y. Liu, F. Odumudu and B. Viray.

Details

Date:
October 15
Time:
12:15 pm - 1:10 pm
Event Category:

Venue

Emmy Noether Room, Millikan 1021, Pomona College
610 N. College Ave.
Claremont, California 91711
+ Google Map

Details

Date:
October 15
Time:
12:15 pm - 1:10 pm
Event Category:

Venue

Emmy Noether Room, Millikan 1021, Pomona College
610 N. College Ave.
Claremont, California 91711
+ Google Map