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. 

Oriented Borel–Moore homologies of toric varieties

  • Toni Annala
  • Mathematics
    Annales 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

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

  • Shoji Yokura
  • Mathematics
    International 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.

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

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

References

SHOWING 1-6 OF 6 REFERENCES

Descent for algebraic cobordism

We prove the exactness of a descent sequence relating the algebraic cobordism groups of a scheme and its envelopes. Analogous sequences for Chow groups and K-theory were previously proved by Gillet.

Toroidal varieties and the weak factorization theorem

We develop the theory of stratified toroidal varieties, which gives, together with the theory of birational cobordisms [73], a proof of the weak factorization conjecture for birational maps in

Algebraic Cobordism

Together with F. Morel, we have constructed in [6, 7, 8] a theory of algebraic cobordism, an algebro-geometric version of the topological theory of complex cobordism. In this paper, we give a survey

Torification and factorization of birational maps

Building on the work of the fourth author in math.AG/9904074, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular

Algebraic cobordism revisited

We define a cobordism theory in algebraic geometry based on normal crossing degenerations with double point singularities. The main result is the equivalence of double point cobordism to the theory