Torsion algebraic cycles and étale cobordism
Copyright policy )Torsion algebraic cycles and étale cobordism
Following an idea of Totaro, we prove that the classical integral cycle class map from algebraic cycles to ��tale cohomology factors through a quotient of $\ell$-adic ��tale 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
- Harvard University United States
Étale homotopy, étale cobordism, Mathematics(all), étale homotopy, 14F20, 14F35 (Secondary), Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Algebraic cycles, Étale cobordism, algebraic cycles, Mathematics - Algebraic Geometry, Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), 14C25 (Primary); 14F20, 14F35 (Secondary), FOS: Mathematics, 14C25 (Primary), Bordism and cobordism theories and formal group laws in algebraic topology, Griffiths group, Algebraic Geometry (math.AG)
Étale homotopy, étale cobordism, Mathematics(all), étale homotopy, 14F20, 14F35 (Secondary), Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Algebraic cycles, Étale cobordism, algebraic cycles, Mathematics - Algebraic Geometry, Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), 14C25 (Primary); 14F20, 14F35 (Secondary), FOS: Mathematics, 14C25 (Primary), Bordism and cobordism theories and formal group laws in algebraic topology, Griffiths group, Algebraic Geometry (math.AG)
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