Algebraic cobordism theory attached to algebraic equivalence

Details Algebraic cobordism theory attached to algebraic equivalence Algebraic cobordism theory attached to algebraic equivalence

2012-03-25

arxiv.org/abs/1203.5508v1

Mathematics

Algebraic Geometry

30 pages

Scientific paper

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 finite coefficients, 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 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.

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