Chow groups of conic bundles in $\mathbb P^5$ and the Generalised Bloch's conjecture

Abstract

Consider the Fano surface of a conic bundle embedded in $\mathbb P^5$. Let $i$ denote the natural involution acting on this surface. In this note we provide an obstruction to the identity action of the involution on the group of algebraically trivial zero cycles modulo rational equivalence on the surface.