no. 6
Oriented Borel–Moore homologies of toric varieties
[Homologies orientées de Borel–Moore des variétés toriques]
Annala, Toni M.1
1 University of British Columbia Department of Mathematics 1984 Mathematics Rd Vancouver, BC V6T 1Z2 (Canada)
Annales de l'Institut Fourier, Tome 71 (2021) no. 6, pp. 2431-2470.

Nous généralisons la formule de Künneth bien connue pour les groupes de Chow au cas d’une théorie homologique orientée de Borel–Moore arbitraire qui vérifient des propriétés de localisation et de descente (par exemple le bordisme algébrique) pour les produits avec une variété torique. En corollaire, nous obtenons un théorème de coefficients universels pour les anneaux de cohomologie opérationnelle. Nous donnons également une nouvelle description, de nature homologique, des groupes d’homologie des variétés toriques lisses, qui nous permet de calculer les groupes de bordisme algébrique de quelques variétés toriques singulières.

We generalize the well known Künneth formula for Chow groups to an arbitrary oriented Borel–Moore homology theory satisfying localization and descent (e.g. algebraic bordism) when taking a product with a toric variety. As a corollary we obtain a universal coefficient theorem for the operational cohomology rings. We also give a new, homological, description for the homology groups of smooth toric varieties, which allows us to compute the algebraic bordism groups of some singular toric varieties.

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DOI : 10.5802/aif.3452
Classification : 14F43, 14C99, 14M25
Keywords: oriented Borel–Moore homology, toric varieties, algebraic bordism
Mot clés : homologie orienté de Borel–Moore, variété torique, cobordisme algébrique
Annala, Toni M. 1

1 University of British Columbia Department of Mathematics 1984 Mathematics Rd Vancouver, BC V6T 1Z2 (Canada) 
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     title = {Oriented {Borel{\textendash}Moore} homologies of toric varieties},
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Annala, Toni M. Oriented Borel–Moore homologies of toric varieties. Annales de l'Institut Fourier, Tome 71 (2021) no. 6, pp. 2431-2470. doi : 10.5802/aif.3452. http://www.numdam.org/articles/10.5802/aif.3452/

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