On the integral Tate conjecture for 1-cycles on the product of a curve and a surface over a finite field

Abstract: Let X be the product of a smooth projective curve C and a smooth projective surface S over a finite field F. Assume the Chow group of zero-cycles on S is just Z over any algebraically closed field extension of F (example : Enriques surface). We give a simple condition on C and S which ensures that the integral Tate conjecture holds for 1-cycles on X. An equivalent formulation is a vanishing result for unramified cohomology of degree 3. This generalizes a result of A. Pirutka (2016). It is a joint work with Federico Scavia (UBC, Vancouver).

algebraic geometry

Audience: researchers in the topic

Warwick algebraic geometry seminar