Bivariant Algebraic Cobordism

Abstract

We associate a bivariant theory to any suitable oriented Borel-Moore homology theory on the category of algebraic schemes or the category of algebraic G-schemes. Applying this to the theory of algebraic cobordism yields operational cobordism rings and operational G-equivariant cobordism rings associated to all schemes in these categories. In the case of toric varieties, the operational T-equivariant cobordism ring may be described as the ring of piecewise graded power series on the fan with coefficients in the Lazard ring.

39 pages

References in corpus (2)

• Algebraic Cobordism of Classifying Spaces
• Cobordism ring of toric varieties

Cited by in corpus (11)

• Bivariant theories in motivic stable homotopy
• Precobordism and cobordism
• K-classes of Brill-Noether loci and a determinantal formula
• A case study of intersections on blowups of the moduli of curves
• Equivariant Grothendieck-Riemann-Roch and localization in operational K-theory
• Oriented bivariant theory II- Algebraic cobordism of $S$-schemes -
• The equivariant $K$-theory and cobordism rings of divisive weighted projective spaces
• Cobordism bicycles of vector bundles
• Co-operational bivariant theory
• Minkowski weights and the Grothendieck group of a toric variety
• Formal Group Rings of Toric Varieties