We study the equivariant cobordism rings for the action of a torus T on smooth varieties over an algebraically closed field of characteristic zero. We prove a theorem describing the rational T-equivariant cobordism rings of smooth projective G-spherical varieties with the action of a maximal torus T of G. As an application, we obtain explicit presentations for the rational equivariant cobordism rings of smooth projective horospherical varieties of Picard number one.
We show that a gauge bounded Cartier algebra has finite complexity. We also give an example showing that the converse does not hold in general.1991 Mathematics Subject Classification. 13A35.
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