Torsion Algebraic Cycles and Étale Cobordism
نویسنده
چکیده
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
منابع مشابه
Torsion algebraic cycles and complex cobordism
Atiyah and Hirzebruch gave the first counterexamples to the Hodge conjecture with integer coefficients. In particular, there is a smooth complex projective variety X of dimension 7 and a torsion element of H(X,Z) which is not the class of a codimension-2 algebraic cycle [4]. In this paper, we provide a more systematic explanation for their examples: for every smooth complex algebraic variety X ...
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