Abelian Varieties Multi-Site Seminar Series: Bianca Viray

  • Date: 11/12/2015
Bianca Viray, University of Washington

University of Washington


An arithmetic intersection formula for denominators of Igusa class polynomials [video]


Igusa class polynomials are the genus 2 analogue of Hilbert class polynomials; their roots are invariants of genus 2 curves that have complex multiplication by a fixed order.  The coefficients of Igusa class polynomials are rational, but, unlike in genus 1, are not integral.  An exact formula, or tight upper bound, for these denominators is needed to compute Igusa class polynomials and has applications to cryptography.  In this talk, we explain how to obtain a formula for the arithmetic intersection number G1.CM(K) and how this results in a bound for denominators of Igusa class polynomials.  We also explain how the formula for G1.CM(K) leads us to a generalization of Gross and Zagier's formula for differences of CM j-invariants.  This is joint work with Kristin Lauter.

Other Information: 

 A video of this event is available on mathtube.org



Bluejeans Connection Info:

Meeting Title: CRG: Explicit methods for abelian varieties meeting Meeting Time: Every second Thursday of the month • from November 12,
2015 • through December 10, 2015 • 11 a.m. MST / 1 hr
        Join Meeting

        (Try your iPhone or Android phone)

Connecting directly from a room system?

1) Dial: or bjn.vc <http://bjn.vc>
2) Enter Meeting ID: 867885727

Just want to dial in on your phone?

1) Direct-dial with my iPhone <tel:+1.408.740.7256+1.408.740.7256,,#867885727%23,%23> or
+1.408.740.7256+1.408.740.7256 <tel:+1.408.740.7256+1.408.740.7256>
+1.888.240.2560+1.888.240.2560 FREE <tel:+1.888.240.2560+1.888.240.2560 FREE> (US Toll Free)
+1.408.317.9253+1.408.317.9253 <tel:+1.408.317.9253+1.408.317.9253> (Alternate number)
(all numbers <http://bluejeans.com/numbers>)
2) Enter Meeting ID: 867885727