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Grothendieck standard conjectures, morphic cohomology and Hodge index theorem

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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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  1. Department of Mathematics, National Tsing Hua University, Hsinchu, 30043, Taiwan

    Jyh-Haur Teh

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  1. Jyh-Haur Teh
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Correspondence to Jyh-Haur Teh.

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Teh, JH. Grothendieck standard conjectures, morphic cohomology and Hodge index theorem. Math. Z. 260, 849–864 (2008). https://doi.org/10.1007/s00209-008-0303-z

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