Chow Rings, Decomposition of the Diagonal, and the Topology by Claire Voisin

By Claire Voisin

In this ebook, Claire Voisin offers an advent to algebraic cycles on complicated algebraic types, to the key conjectures concerning them to cohomology, or even extra accurately to Hodge buildings on cohomology. the amount is meant for either scholars and researchers, and never purely offers a survey of the geometric equipment constructed within the final thirty years to appreciate the well-known Bloch-Beilinson conjectures, but additionally examines fresh paintings via Voisin. The e-book specializes in vital gadgets: the diagonal of a variety—and the partial Bloch-Srinivas style decompositions it will possibly have looking on the dimensions of Chow groups—as good as its small diagonal, that's the proper item to think about that allows you to comprehend the hoop constitution on Chow teams and cohomology. An exploration of a sampling of contemporary works by way of Voisin appears to be like on the relation, conjectured normally by means of Bloch and Beilinson, among the coniveau of normal entire intersections and their Chow teams and a truly specific estate happy by way of the Chow ring of K3 surfaces and conjecturally by means of hyper-Kähler manifolds. particularly, the e-book delves into arguments originating in Nori's paintings which have been additional constructed by way of others.

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