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arXiv · 1808.08385

Motivic Gau{\ss}-Bonnet formulas

Marc Levine·Arpon Raksit
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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.

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Marc Levine, Arpon Raksit. 2018-08-25. Motivic Gau{\ss}-Bonnet formulas. https://doi.org/10.2140/ant.2020.14.1801

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