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In this text we prove that if an abelian variety $A$ admits of an embeddinginto the Jacobian of a smooth projective curve $C$, and if we consider $\Th_A$to be the divisor $\Th_C\cap A$, where $\Th_C$ denotes the theta divisor of$J(C)$, then the embedding of $\Th_A$ into $A$ induces an injectivepush-forward homomorphism at the level of Chow groups. We show that this is thecase for every principally polarized abelian varieties.

Theta divisors of abelian varieties and push-forward homomorphism at the level of Chow groups