Algebra & Number Theory

Bivariant algebraic cobordism

José González and Kalle Karu

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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.

Article information

Algebra Number Theory, Volume 9, Number 6 (2015), 1293-1336.

Received: 28 January 2013
Revised: 21 April 2015
Accepted: 20 May 2015
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]
Secondary: 14C15: (Equivariant) Chow groups and rings; motives 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) 14M25: Toric varieties, Newton polyhedra [See also 52B20] 55N22: Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90] 57R85: Equivariant cobordism

algebraic cobordism bivariant and operational theories operational (equivariant) cobordism operational equivariant cobordism of toric varieties


González, José; Karu, Kalle. Bivariant algebraic cobordism. Algebra Number Theory 9 (2015), no. 6, 1293--1336. doi:10.2140/ant.2015.9.1293.

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