PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Robert Vaughan, Mihran Papikian, Ae Ja Yee.

Title:Palindromic properties of curves and explicit descent obstructions
Seminar:Algebra and Number Theory Seminar
Speaker:James Stankewicz, University of Copenhagen
Abstract:
For most curves that you might think of, it is possible to find a twist which has a rational point. For the first time we exhibit an infinite family of curves over the rational numbers for which this explicitly does not apply. That is to say that we find Shimura curves C whose lack of rational points is palindromic or preserved by twists. Using this family of curves, we find a related set of twists of Shimura curves which all violate the Hasse Principle. Moreover, rather than using Faltings theorem or a density result to say that some infinite subcollection violates the Hasse Principle, we explicitly identify violations using the descent obstruction.

Room Reservation Information

Room Number:MB106
Date:01 / 16 / 2014
Time:11:15am - 12:05pm