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    Title      l  Algebraic cobordism theory attached to algebraic equivalence
    Author   l  Amalendu Krishna, Jinhyun Park
    Date   l  2012-03-26
    Category   l  ASARC-Preprint-12-01
    Download    l 1332721464_0.789347.pdf  
Abstract. After the algebraic cobordism theory of Levine-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 zero-th semi-topological K-groups. We also show that with nite coecients,
this theory agrees with the algebraic cobordism theory.
We compute our cobordism theory for some low dimensional or special types of
varieties. The results on in nite generation of some Griths groups by Clemens and
on smash-nilpotence by Voevodsky and Voisin are also lifted and reinterpreted in terms
of this cobordism theory.

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