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Selmer groups and class groups

New Geometric Techniques in Number Theory July 01, 2013 - July 12, 2013

July 05, 2013 (02:45 PM PDT - 03:15 PM PDT)
Speaker(s): Kestutis Cesnavicius (Centre National de la Recherche Scientifique (CNRS))
Location: MSRI: Simons Auditorium
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Abstract 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.
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