2010/10/29 by Amalendu Krishna, Krishna, Amalendu
Mathematics · #14C25 #19E15 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C25 #msc:19E15
paper · pdf · doi:10.48550/arxiv.1010.6182
arxiv created 2010/10/29 · arxiv updated 2010/11/01
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.