Pushforwards of Chow groups of smooth ample divisors, with an emphasis on Jacobian varieties

Abstract

With a homological Lefschetz conjecture in mind, we prove the injectivity of the pushforward morphism on low-dimensional rational Chow groups, induced by the closed embedding of an ample divisor, namely, the Theta divisor inside the Jacobian variety 𝐽(𝐶). Here, 𝐶 is a smooth irreducible complex projective curve.