Lori Watson (Wake Forest University)

Québec-Vermont Number Theory Seminar

Title: Hasse Principle Violations in Families of Twists of Superelliptic Curves.

Abstract: For a nice curve C defined over Q it is in general very difficult to determine the set of rational points on the curve. Even determining whether rational points exist is difficult. Proving the existence of rational points becomes considerably easier when the Hasse Principle is known to hold. In this talk, we will discuss violations of the Hasse Principle within families of twists of superelliptic curves and, conditional on the abc conjecture, give simple criteria for determining when the Hasse Principle will hold within such families. Based in part on joint work with Pete L. Clark. 

For Zoom details, please contact: martinez [at] crm.umontreal.ca