Grothendieck standard conjectures,morphic cohomology and Hodge index theorem |
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Authors: | Jyh-Haur Teh |
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Institution: | (1) Department of Mathematics, National Tsing Hua University, Hsinchu, 30043, Taiwan |
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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. |
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Keywords: | |
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