Date: Monday, February 18, 2013
Location: 4096 East Hall (3:00 PM to 5:00 PM)
Title: Reductions of CM j-invariants modulo p
Abstract: The moduli space of elliptic curves contains infinitely many algebraic points that correspond to curves with complex multiplication. In 1985, Gross and Zagier proved that the pp-adic valuation of the difference of two CM j- invariants is exactly half the sum (over n) of the number of isomorphisms between the corresponding elliptic curves modulo pp^n. Using this relation, Gross and Zagier proved an elegant formula for the factorization of the norm of a difference of CM j-invariants, assuming that the CM orders are maximal and have relatively prime discriminants. We generalize their result to the case where one order has squarefree discriminant and the other order is arbitrary. If time permits, we will explain how this result can be used to answer a similar question in genus 2. This is joint work with Kristin Lauter.
Speaker: Bianca Viray
Institution: Brown University
Event Organizer: mityab@umich.edu
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