Torsion algebraic cycles and etale cobordism

Details Torsion algebraic cycles and etale cobordism Torsion algebraic cycles and etale cobordism

2009-11-03

arxiv.org/abs/0911.0584v3

Mathematics

Algebraic Geometry

23 pages (initially 22 p.); slight change of the introduction; correction of typos

Scientific paper

Following an idea of Totaro, we prove that the classical integral cycle class map from algebraic cycles to \'etale cohomology factors through a quotient of $\ell$-adic \'etale 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.

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