Let A be an abelian variety over a number field K. If A has nontrivial (resp. full) K-rational p-torsion for a prime p, exploiting the fppf cohomological approach to Selmer groups, we obtain inequalities bounding the size of the p-Selmer group of A from below (resp. above) in terms of the size of the p-torsion subgroup of the ideal class group of K. When K varies in a family of field extensions, these inequalities relate the growth of Selmer groups to that of class groups; I will discuss such relations in several different settings.
Tuesday, August 27th, at 4:00pm in HBH 227
Return to talks from Fall 2013