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

Title: | Dyadic Torsion of Elliptic Curves |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Jeffrey Yelton, Penn State |

Abstract: |

The image of the action of Galois on \ell-adic Tate modules of abelian varieties has been a topic of considerable study. A particularly interesting case is that of hyperelliptic jacobians for \ell = 2. Certain results such as Serre's celebrated \open image theorem" have shown that, under certain conditions, the image of Galois in the symplectic group of automorphisms of the Tate module is open of finite index. However, little is known about exactly how the Galois group acts on the field of definition of dyadic torsion of a given hyperelliptic jacobian. In this talk, I will give formulas for the field of definition of dyadic torsion of certain elliptic curves, as well as describe the structure of the Galois group of this fi eld extension and how it acts on certain generators. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 09 / 19 / 2013 |

Time: | 11:15am - 12:05pm |