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Abstract
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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
-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.
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Keywords
algebraic cobordism, bivariant and operational theories,
operational (equivariant) cobordism, operational
equivariant cobordism of toric varieties
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Mathematical Subject Classification 2010
Primary: 14C17
Secondary: 14C15, 14F43, 14M25, 55N22, 57R85
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Milestones
Received: 28 January 2013
Revised: 21 April 2015
Accepted: 20 May 2015
Published: 7 September 2015
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