ICTP Mathematics Seminar - Thursday 1, February, at 14.00 hrs (Céline Maistret, Univ. of Bristol)

[ICTP Math Section]

M A T H E M A T I C S   S E M I N A R S  2018


Thursday 1, February, at 14.00 hrs.


Céline Maistret (University of Bristol)


Parity of ranks of abelian surfaces


Abstract:  Let K be a number field and A/K an abelian surface. By the 
Mordell-Weil theorem, the group of K-rational points on A is finitely 
generated and as for elliptic curves, its rank is predicted by the Birch 
and Swinnerton-Dyer conjecture. A basic consequence of this conjecture 
is the parity conjecture: the sign of the functional equation of the 
L-series determines the parity of the rank of A/K. Under suitable local 
constraints and finiteness of the Shafarevich-Tate group, we prove the 
parity conjecture for principally polarized abelian surfaces. We also 
prove analogous unconditional results for Selmer groups.


VENUE:  Stasi Seminar Room(ICTP Leonardo da Vinci Building, first floor)