Derived cycle classes

Abstract: Let X be a smooth complex algebraic variety. In contrast with the situation for the singular homology groups H_*(X), the construction of intersection products on the Chow groups of X is subtle due to the comparative difficulty in dealing with non-transverse intersections. I will explain one way to deal with this problem by considering cycle classes that come from derived algebraic geometry. In combination with the algebraic analogue of Steenrod's problem on resolution of singularities of homology classes (which holds by Hironaka), this yields a new construction of cup products in Chow groups. Time permitting, I may also discuss how derived cycle classes arise in motivic homotopy theory.

algebraic topology

Audience: researchers in the topic

MIT topology seminar

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