Some remarks on Chow correspondences

We study, in the context of Voevodsky’s triangulated category of motives, several adequate equivalence relations (in the sense of Samuel) on the graded Chow ring $CH^\ast (X\times Y)$ for $X$, $Y$ smooth projective varieties over a field.

💡 Research Summary

The paper investigates the relationship between Chow correspondences and regular homomorphisms arising from the Albanese map within Voevodsky’s triangulated category of motives DMₖ. Let X and Y be smooth projective varieties over an algebraically closed field k, with dimensions d and d_Y respectively. For a Chow correspondence Λ∈CH^{d+n}(X×Y) the author defines a homomorphism

 ψ : CH_{d_Y‑n}(Y) → Alb(X)(k), γ ↦ alb_X(Λ(γ) − deg(Λ(γ))