For more information about this meeting, contact Karl Schwede.

Title: | F-thresholds of elliptic curves (Algebra and Number Theory Seminar) |

Seminar: | Combinatorics/Partitions Seminar |

Speaker: | Bhargav Bhatt, University of Michigan |

Abstract: |

F-pure thresholds are certain invariants of singularities in
characteristic p that are supposed to mimic the behaviour of log
canonical thresholds in characteristic 0. In particular, there exists
theorems and deep conjectures relating the two numbers when one
specialises from characteristic 0 to positive characteristic, provided
the prime p is allowed to suitably large. In this talk, we will
introduce these numbers, and discuss some calculations in a fixed
characteristic p. Contrary to the conjectural situation where the
prime p is allowed to vary, we will show that when p is fixed, the
behaviour of these numbers is closely related to the arithmetic of the
singularities. The main example discussed will be the cone on an
elliptic curve, where the invariant is completely determined with the
aid of some geometry (especially, the deformation theory) of elliptic
curves; this answers a question raised by M. Mustata. Time permitting,
we will discuss some higher dimensional calculations.
This is a non-standard meeting of the Algebra and Number Theory seminar. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 04 / 19 / 2011 |

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