On the Hodge group and invariant cycles of a simple Abelian variety with a stable reduction of odd toric rank

Abstract

The semi-simplicity of the Hodge group is proved for a simple Abelian variety with a stable reduction of odd toric (reductive) rank. If, besides, the dimension of the Abelian variety is an odd integer, then the Hodge conjecture on algebraic cycles holds for it.

References in corpus (1)

• Hodge groups of abelian varieties with purely multiplicative reduction