For more information about this meeting, contact Karl Schwede, 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 |