Gereon Quick: Torsion algebraic cycles and etale cobordism

Abstract: We show that the classical integral cycle class map from algebraic cycles to étale cohomology factors through a quotient of l-adic étale cobordism over an algebraically closed field of positive characteristic. This shows that there is a strong topological obstruction for cohomology classes to be algebraic and that examples of Atiyah, Hirzebruch and Totaro also work in positive characteristic.