2006/03/09 by Wenchuan Hu, Hu, Wenchuan
Mathematics · #14C25 #14F43 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14C25 #msc:14F43
paper · pdf · doi:10.48550/arxiv.math/0603203
16 pages
arxiv created 2006/03/09 · openalex publication_date 2006/03/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first part of this paper, we show that the assertion "TpHk(X,Q)=GpHk(X,Q)" (which is called the Friedlander-Mazur conjecture) is a birationally invariant statement for smooth projective varieties X when p=dim(X)-2 and when p=1. We also establish the Friedlander-Mazur conjecture in certain dimensions. More precisely, for a smooth projective variety X, we show that the topological filtration TpH2p+1(X,Q) coincides with the geometric filtration GpH2p+1(X,Q) for all p. (Friedlander and Mazur had previously shown that TpH2p(X,Q)=GpH2p(X,Q)). As a corollary, we conclude that for a smooth projective threefold X, TpHk(X,Q)=GpHk(X,Q) for all k≥ 2p≥ 0 except for the case p=1,k=4. Finally, we show that the topological and geometric filtrations always coincide if Suslin's conjecture holds.