Squarefree parts of polynomial values

04/15/2014 - 12:15pm
04/15/2014 - 1:10pm
David Krumm (Claremont McKenna College)

Let C be a hyperelliptic curve defined over the rational numbers, and consider the set S of all squarefree integers d such that the quadratic twist of C by d has a rational point. In this talk we will discuss the question of whether, given a prime number p, the set S contains representatives from all congruence classes modulo p. When C has genus 0 this question can be answered using elementary number theory, but for higher genera it seems to require the use of big conjectures in arithmetic geometry.

Mudd Science Library 126, Pomona College