#### Vol. 9, No. 6, 2015

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Bivariant algebraic cobordism

### José Luis González and Kalle Karu

Vol. 9 (2015), No. 6, 1293–1336
##### 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