By Claire Voisin
In this publication, Claire Voisin offers an advent to algebraic cycles on complicated algebraic types, to the foremost conjectures bearing on them to cohomology, or even extra accurately to Hodge buildings on cohomology. the quantity is meant for either scholars and researchers, and never in basic terms provides a survey of the geometric equipment built within the final thirty years to appreciate the well-known Bloch-Beilinson conjectures, but additionally examines contemporary paintings by means of Voisin. The publication specializes in valuable items: the diagonal of a variety—and the partial Bloch-Srinivas sort decompositions it could have counting on the dimensions of Chow groups—as good as its small diagonal, that is the appropriate item to contemplate to be able to comprehend the hoop constitution on Chow teams and cohomology. An exploration of a sampling of contemporary works through Voisin appears to be like on the relation, conjectured ordinarily by means of Bloch and Beilinson, among the coniveau of basic entire intersections and their Chow teams and a truly specific estate chuffed by way of the Chow ring of K3 surfaces and conjecturally by means of hyper-Kähler manifolds. specifically, the ebook delves into arguments originating in Nori's paintings which were additional built via others.
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Extra resources for Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187) (Annals of Mathematics Studies)
Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187) (Annals of Mathematics Studies) by Claire Voisin