Adrian Vasiu (Binghampton)
Good reductions of abelian varieties over number fields
Abstract: Complex abelian varieties are the algebraic version of compact,
connected, commutative complex Lie groups.
They are embeddable into projective spaces and have many types of
invariants. For instance, their Mumford--Tate groups are reductive groups
over Q which can be viewed as analytic invariants.
When the complex abelian varieties are definable over number fields, one
associates to them several arithmetic invariants
which encode their good reductions at finite primes. An old conjecture of
Morita pertains to the impact of the Morita--Tate groups on the mentioned
arithmetic invariants. We report on a solution of this
conjecture in a very general case.