I will construct a family of Enriques surfaces parametrized by P^1 such that any multi-section has even degree over the base P^1. This gives the first example of an O-acyclic variety over the function field of a complex curve, whose index is not equal to one, and an affirmative answer to a question of Colliot-Thelene and Voisin. I will also discuss applications to related problems, including the integral Hodge conjecture and Murre's question on universality of the Abel-Jacobi maps. This is joint work with John Christian Ottem. Speaker(s): Fumiaki Suzuki (UCLA)