Motivic Bivariant Characteristic Classes

@article{Schuermann2010MotivicBC,
  title={Motivic Bivariant Characteristic Classes},
  author={Joerg Schuermann and Shoji Yokura},
  journal={arXiv: Algebraic Geometry},
  year={2010}
}
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7 Citations
Background Citations
1
Methods Citations
1

7 Citations

Citation Type

Citation Type

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 $M$…
Bivariant Versions of Algebraic Cobordism
We define four distinct oriented bivariant theories associated with algebraic cobordism in its two versions (the axiomatic $\Omega$ and the geometric $\omega$), when applied to quasi-projective…
Motivic Milnor classes
The Milnor class is a generalization of the Milnor number, defined as the difference (up to sign) of Chern--Schwartz--MacPherson's class and Fulton--Johnson's canonical Chern class of a local…
Bivariant algebraic cobordism with bundles
The purpose of this paper is to study an extended version of bivariant derived algebraic cobordism where the cycles carry a vector bundle on the source as additional data. We show that, over a field…
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…
Naive motivic Donaldson-Thomas type Hirzebruch classes and some problems
Donaldson-Thomas invariant is expressed as the weighted Euler characteristic of the so-called Behrend (constructible) function. In (2) Behrend introduced a Donaldson-Thomas type invariant for a mor-…
Topics of motivic characteristic classes

References

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Motivic Milnor classes
The Milnor class is a generalization of the Milnor number, defined as the difference (up to sign) of Chern--Schwartz--MacPherson's class and Fulton--Johnson's canonical Chern class of a local…
HIRZEBRUCH CLASSES AND MOTIVIC CHERN CLASSES FOR SINGULAR SPACES
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Motivic Bivariant Characteristic Classes and Related Topics
We have recently constructed a bivariant analogue of the motivic Hirzebruch classes. A key idea is the construction of a suitable universal bivariant theory in the algebraic-geometric (or compact…
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