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Algebraic cobordism theory attached to algebraic equivalence

Published online by Cambridge University Press:  06 March 2013

Amalendu Krishna  and
Jinhyun Park
Amalendu Krishna
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Colaba, Mumbai, 400 005, Indiaamal@math.tifr.res.in
Jinhyun Park
Affiliation:
Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, Republic of Korea (South)jinhyun@mathsci.kaist.ac.krjinhyun@kaist.edu
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Abstract

Based on the algebraic cobordism theory of Levine and Morel, we develop a theory of algebraic cobordism modulo algebraic equivalence.

We prove that this theory can reproduce Chow groups modulo algebraic equivalence and the semi-topological K0-groups. We also show that with finite coefficients, this theory agrees with the algebraic cobordism theory.

We compute our cobordism theory for some low dimensional varieties. The results on infinite generation of some Griffiths groups by Clemens and on smash-nilpotence by Voevodsky and Voisin are also lifted and reinterpreted in terms of this cobordism theory.

Keywords

cobordismChow groupK-theoryalgebraic cycleGriffiths groupPrimary 14F43Secondary 55N22

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Type
Research Article
Information
Journal of K-Theory , Volume 11 , Issue 1 , February 2013 , pp. 73 - 112
Copyright
Copyright © ISOPP 2013

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