Algebraic cobordism theory attached to algebraic equivalence

Krishna, Amalendu ; Park, Jinhyun (2013) Algebraic cobordism theory attached to algebraic equivalence Journal of K-Theory, 11 (01). pp. 73-112. ISSN 1865-2433

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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.

Item Type:Article
Source:Copyright of this article belongs to Cambridge University Press.
Keywords:Cobordism; Chow Group; K-Theory; Algebraic Cycle; Griffiths Group
ID Code:102459
Deposited On:09 Mar 2018 10:47
Last Modified:09 Mar 2018 10:47

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