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Motivic integration and projective bundle theorem in morphic cohomology

Published online by Cambridge University Press:  01 September 2009

JYH-HAUR TEH
JYH-HAUR TEH*
Affiliation:
Department of Mathematics, National Tsing Hua University, No. 101, Sec 2, Kuang Fu Road, Hsinchu 30043, Taiwan. e-mail: [email protected]
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Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 2 , September 2009 , pp. 295 - 321
Copyright
Copyright © Cambridge Philosophical Society 2009

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