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arXiv · 2404.16378

Quadratic Euler Characteristic of Symmetric Powers of Curves

Lukas F. Bröring·Anna M. Viergever
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Abstract

We compute the quadratic Euler characteristic of the symmetric powers of a smooth, projective curve over any field $k$ that is not of characteristic two, using the Motivic Gauss-Bonnet Theorem of Levine-Raksit. As an application, we show over a field of characteristic zero that the power structure on the Grothendieck-Witt ring introduced by Pajwani-P\'al computes the compactly supported $\mathbb{A}^1$-Euler characteristic of symmetric powers for all curves.

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Lukas F. Bröring, Anna M. Viergever. 2024-04-25. Quadratic Euler Characteristic of Symmetric Powers of Curves. https://arxiv.org/abs/2404.16378

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