English

Motivic characteristic classes for singular schemes

Algebraic Geometry 2022-11-02 v2 Algebraic Topology K-Theory and Homology

Abstract

We construct characteristic classes for singular algebraic varieties in motivic Borel-Moore homology, extending the motivic Euler class of the tangent bundle defined for smooth varieties. The two classes we define refine, in the setting of motivic homotopy theory, the top degree of the class constructed by Brasselet-Schuermann-Yokura in G-theory, and the top degree of the pro-CSM class constructed by Aluffi in pro-Chow groups. We deduce an extension of the motivic Gauss-Bonnet formula to non-smooth proper varieties.

Keywords

Cite

@article{arxiv.2208.14440,
  title  = {Motivic characteristic classes for singular schemes},
  author = {Ran Azouri},
  journal= {arXiv preprint arXiv:2208.14440},
  year   = {2022}
}

Comments

v2: paper rearranged with title and abstract modified; 17 pages; comments welcome

R2 v1 2026-06-28T00:25:51.653Z