Algebra & Number Theory
- Algebra Number Theory
- Volume 9, Number 6 (2015), 1293-1336.
Bivariant algebraic cobordism
We associate a bivariant theory to any suitable oriented Borel–Moore homology theory on the category of algebraic schemes or the category of algebraic -schemes. Applying this to the theory of algebraic cobordism yields operational cobordism rings and operational -equivariant cobordism rings associated to all schemes in these categories. In the case of toric varieties, the operational -equivariant cobordism ring may be described as the ring of piecewise graded power series on the fan with coefficients in the Lazard ring.
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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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
González, José; Karu, Kalle. Bivariant algebraic cobordism. Algebra Number Theory 9 (2015), no. 6, 1293--1336. doi:10.2140/ant.2015.9.1293. https://projecteuclid.org/euclid.ant/1510842372