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

O. V Oreshkina

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arXiv · 1809.01910

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

O. V Oreshkina

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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.

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O. V Oreshkina. 2018-09-06. On the Hodge group and invariant cycles of a simple Abelian variety with a stable reduction of odd toric rank. https://arxiv.org/abs/1809.01910

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