分野別セミナー

The most classical 'finiteness result' on abelian varieties was conjectured by Shafarevich and proven by Faltings: The number of isomorphism classes of abelian varieties with fixed dimension,
field of definition, and reduction type is finite. In this talk,we discuss joint work with Akio Tamagawa on a different style of finiteness result, where the reduction type is allowed to vary in a controlled fashion. In exchange for this freedom, we place an arithmetic constraint on the structure of the pro-p torsion of
the abelian variety. Conjecturally, the number of isomorphism classes should still be finite. We prove this in certain cases, and explain the motivations for this conjecture in terms of Galois representations
and a long-standing question of Ihara.