Motivic integration and projective bundle theorem in morphic cohomology

Details Motivic integration and projective bundle theorem in morphic cohomology Motivic integration and projective bundle theorem in morphic cohomology

2006-10-23

arxiv.org/abs/math/0610672v3

Mathematics

Algebraic Geometry

24 pages

Scientific paper

We reformulate the construction of Kontsevich's completion and use Lawson homology to define many new motivic invariants. We show that the dimensions of subspaces generated by algebraic cycles of the cohomology groups of two $K$-equivalent varieties are the same, which implies that several conjectures of algebraic cycles are $K$-statements. We define stringy functions which enable us to ask stringy Grothendieck standard conjecture and stringy Hodge conjecture. We prove a projective bundle theorem in morphic cohomology for trivial bundles over any normal quasi-projective varieties.

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