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The Grothendieck standard conjectures, morphic cohomology and the Hodge index theorem
, 2005
"... From morphic cohomology, we produce a finite sequence of conjectures, called morphic conjectures, which terminates at the Grothendieck standard conjecture of Lefschetz type. We generalize the notions of numerical equivalence and homological equivalence of algebraic cycles to morphic numerical equiva ..."
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Cited by 3 (3 self)
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From morphic cohomology, we produce a finite sequence of conjectures, called morphic conjectures, which terminates at the Grothendieck standard conjecture of Lefschetz type. We generalize the notions of numerical equivalence and homological equivalence of algebraic cycles to morphic numerical equivalence and morphic homological equivalence of elements in morphic cohomology groups. Some equivalent forms of the conjectures are provided. In particular, the equivalence of these two equivalence relations is equivalent to the validity of the corresponding morphic conjecture. All morphic conjectures are proved for abelian varieties. We endow the morphic cohomology groups of a smooth projective variety with an inductive limit of mixed Hodge structure and define the morphic Hodge numbers. We generalize the notion of signature to morphic signatures, and for each morphic signature, by assuming the corresponding morphic conjecture, a result analogous to the Hodge index theorem is proved. We prove a conjecture in rational coefficients of Friedlander and Lawson by assuming the Grothendieck standard conjecture B.
unknown title
, 2008
"... Motivic integration and projective bundle theorem in morphic cohomology ..."
K^sst for certain . . .
, 2005
"... In this paper we compute Lawson homology groups and semitopological Ktheory for some threefolds and fourfolds. We consider smooth complex projective varieties whose zero cycles are supported on a proper subvariety. Rationally connected varieties are examples of such varieties. The computation make ..."
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In this paper we compute Lawson homology groups and semitopological Ktheory for some threefolds and fourfolds. We consider smooth complex projective varieties whose zero cycles are supported on a proper subvariety. Rationally connected varieties are examples of such varieties. The computation makes use of a technique of Bloch and Srinavas, of the BlochKato theorem and of the spectral sequence