Grothendieck standard conjectures, morphic cohomology and Hodge index theorem

2005/12/12 by Jyh-Haur Teh, Teh, Jyh-Haur
Mathematics · #14C25 #14C30 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14C25 #msc:14C30

paper · pdf · doi:10.48550/arxiv.math/0512232

17 pages. Some results are added and simplified

openalex publication_date 2005/12/12 · arxiv created 2007/10/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using morphic cohomology, we produce a sequence of conjectures, called morphic conjectures, which terminates at the Grothendieck standard conjecture A. A refinement of Hodge structures is given, and with the assumption of morphic conjectures, we prove a Hodge index theorem. We answer a question of Friedlander and Lawson by assuming the Grothendieck standard conjecture B and prove that the topological filtration from morphic cohomology is equal to the Grothendieck arithmetic filtration for some cases.

Related

• Hodge index theorem for arithmetic cycles of codimension one
• Hodge number polynomials for nearby and vanishing cohomology
• Polarizations and Grothendieck's Standard Conjectures
• Motivic integration and projective bundle theorem in morphic cohomology
• Partial Cohomologically Complete Intersections via Hodge Theory