Bivariant algebraic cobordism

González, José; Karu, Kalle

doi:10.2140/ant.2015.9.1293

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Bivariant algebraic cobordism

José Luis González and Kalle Karu

Vol. 9 (2015), No. 6, 1293–1336

DOI: 10.2140/ant.2015.9.1293

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.

Keywords

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

Mathematical Subject Classification 2010

Primary: 14C17

Secondary: 14C15, 14F43, 14M25, 55N22, 57R85

Milestones

Received: 28 January 2013

Revised: 21 April 2015

Accepted: 20 May 2015

Published: 7 September 2015

Authors

José Luis González
Department of Mathematics Yale University 10 Hillhouse Avenue New Haven, CT 06511 United States

Kalle Karu
Department of Mathematics University of British Columbia 1984 Mathematics Road Vancouver, BC V6T 1Z2 Canada

Vol. 9, No. 6, 2015