Torsion algebraic cycles and etale cobordism

2009/11/03 by Gereon Quick, Quick, Gereon
Mathematics · #14C25 (Primary) #14F20 #14F35 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C25 #msc:14F20 #msc:14F35

paper · pdf · doi:10.48550/arxiv.0911.0584

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

arxiv created 2010/01/06 · arxiv updated 2010/01/07

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 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.

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