PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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