Motivic Gau{\ss}-Bonnet formulas
Algebraic Geometry
2020-08-26 v3 Algebraic Topology
Abstract
The apparatus of motivic stable homotopy theory provides a notion of Euler characteristic for smooth projective varieties, valued in the Grothendieck-Witt ring of the base field. Previous work of the first author and recent work of D\'eglise-Jin-Khan establishes a "Gau\ss-Bonnet formula" relating this Euler characteristic to pushforwards of Euler classes in motivic cohomology theories. In this paper, we apply this formula to SL-oriented motivic cohomology theories to obtain explicit characterizations of this Euler characteristic. The main new input is a unicity result for pushforward maps in SL-oriented theories, identifying these maps concretely in examples of interest.
Cite
@article{arxiv.1808.08385,
title = {Motivic Gau{\ss}-Bonnet formulas},
author = {Marc Levine and Arpon Raksit},
journal= {arXiv preprint arXiv:1808.08385},
year = {2020}
}
Comments
Final version-to appear in Algebra & Number Theory