Grothendieck standard conjectures, morphic cohomology and Hodge index theorem

Details Grothendieck standard conjectures, morphic cohomology and Hodge index theorem Grothendieck standard conjectures, morphic cohomology and Hodge index theorem

2005-12-12

arxiv.org/abs/math/0512232v4

Mathematics

Algebraic Geometry

17 pages. Some results are added and simplified

Scientific paper

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.

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