# Projectivity in Algebraic Cobordism

@article{LuisGonzalez2015ProjectivityIA, title={Projectivity in Algebraic Cobordism}, author={Jose Luis Gonzalez and Kalle Karu}, journal={Canadian Journal of Mathematics}, year={2015}, volume={67}, pages={639 - 653} }

Abstract The algebraic cobordism group of a scheme is generated by cycles that are proper morphisms from smooth quasiprojective varieties. We prove that over a field of characteristic zero the quasiprojectivity assumption can be omitted to get the same theory.

## 5 Citations

### Oriented Borel–Moore homologies of toric varieties

- MathematicsAnnales de l'Institut Fourier
- 2022

We generalize the K\"unneth formula for Chow groups to an arbitrary OBM-homology theory satisfying descent (e.g. algebraic cobordism) when taking a product with a toric variety. As a corollary we…

### Fe b 20 18 Oriented Borel-Moore homologies of toric varieties

- Mathematics
- 2018

We generalize the Künneth formula for Chow groups obtained in [6] and [7] to an arbitrary OBM-homology theory satisfying descent (e.g. algebraic cobordism) when taking a product with a toric variety.…

### Oriented bivariant theory, II: Algebraic cobordism of S-schemes

- MathematicsInternational Journal of Mathematics
- 2019

This is a sequel to our previous paper “Oriented bivariant theory, I”. In 2001, Levine and Morel constructed algebraic cobordism for (reduced) schemes [Formula: see text] of finite type over a base…

### Cobordism bicycles of vector bundles.

- Mathematics
- 2019

The main ingredient of the algebraic cobordism of M. Levine and F. Morel is a cobordism cycle of the form $(M \xrightarrow {h} X; L_1, \cdots, L_r)$ with a proper map $h$ from a smooth variety $M$…

### Enriched categories of correspondences and characteristic classes of singular varieties

- MathematicsFundamenta Mathematicae
- 2021

For the category $\mathscr V$ of complex algebraic varieties, the Grothendieck group of the commutative monoid of the isomorphism classes of correspondences $X \xleftarrow f M \xrightarrow g Y$ with…

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