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