2009 Number Theory Seminar - 10

  • Date: 03/12/2009
Nils Bruin (SFU)

Simon Fraser University


Visibility of Sha[3] in genus-2 jacobians


In [Mazur, Visualizing elements of order three in the Shafarevich-Tate
group, Asian J. Math. 3 (1999), no. 1, 221-232], Mazur proves that any
element in Sha[3](E/K) can be made visible in an abelian surface. Mazur
did not comment on whether this surface can be taken to be a Jacobian
of a genus 2 curve, however. His construction does not prove that it
can, but with an easy observation, one can actually see that it is
possible. In this talk, I will explain what Mazur proved and what the
easy observation is. This is joint work with Sander Dahmen (SFU/UBC).
Note that we will move to room K9509 for this second talk.


4:10pm-5:00pm, Room ASB 10900 (IRMACS)