Torsion algebraic cycles and etale cobordism
arXiv:0911.0584
Abstract
Following an idea of Totaro, we prove that the classical integral cycle class map from algebraic cycles to étale cohomology factors through a quotient of -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.
23 pages (initially 22 p.); slight change of the introduction; correction of typos