Equivariant Cobordism for Torus Actions

Details Equivariant Cobordism for Torus Actions Equivariant Cobordism for Torus Actions

2010-10-29

arxiv.org/abs/1010.6182v1

Mathematics

Algebraic Geometry

Scientific paper

We study the equivariant cobordism theory of schemes for torus actions. We give the explicit relation between the equivariant and the ordinary cobordism of schemes with torus action. We deduce analogous results for action of arbitrary connected linear algebraic groups. We prove some structure theorems for the equivariant and ordinary cobordism of schemes with torus action and derive important consequences. We establish the localization theorems in this setting. These are used to describe the structure of the ordinary cobordism ring of certain smooth projective varieties.

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