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26 April 2024 |
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Equivariant Algebraic Cobordism and Equivariant Formal Group Law | | Chun Lung Liu
; | | Date: |
9 May 2013 | | Abstract: | We introduce an equivariant algebraic cobordism theory Omega^G for algebraic
varieties with G action, where G is a split diagonalizable group scheme over a
field k. It is done by combining the construction of the algebraic cobordism
theory Omega by F. Morel and M. Levine, with the notion of (G, F) formal group
law with respect to a complete G universe and complete G flag F as introduced
by M. Cole, J. P. C. Greenlees and I. Kriz. In particular, we use their
corresponding representing ring L_G(F) in place of the Lazard ring L. We show
that localization property and homotopy invariance property hold in Omega^G.
We also prove the surjectivity of the canonical map from L_G(F) to
Omega^G(Spec k). Moreover, we give some comparison results with Omega, the
equivariant algebraic cobordism theory introduced by J. Heller and J. Malagon
Lopez, the equivariant K theory and equivariant cobordism theory by Tom Dieck
(when k = C). Finally, we show that our definition of Omega^G is independent
of the choice of F. | | Source: | arXiv, 1305.2053 | | Services: | Forum | Review | PDF | Favorites | |
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