Parity of ranks of abelian varieties
Adam Morgan (University of Glasgow )
Wednesday 28th November, 2018 16:00-17:00 Maths 311B
For an abelian variety A over a number field K, the Mordell-Weil theorem states that the group of K-points of A is a finitely generated abelian group. The parity conjecture predicts that the rank of this group modulo 2 can be determined from an easily computable quantity related to the L-function of the abelian variety, namely its global root number. We will survey what is known about the parity conjecture, explain some interesting applications, and show how one may prove (a variant) of this conjecture over quadratic extensions of the original number field.