曲线对称幂的二次欧拉特性。

IF 0.6 4区数学 Q3 MATHEMATICS

Manuscripta Mathematica Pub Date : 2025-01-01 Epub Date: 2025-03-20 DOI:10.1007/s00229-025-01623-0

Lukas F Bröring, Anna M Viergever

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引用次数: 0

摘要

我们利用Levine-Raksit的动机高斯-博内定理，计算了任意场k上不具有特征二的光滑投影曲线的对称幂的二次欧拉特征。作为一个应用，我们证明了Pajwani-Pál引入的Grothendieck-Witt环上的幂结构计算了所有曲线对称幂的紧支A 1 -欧拉特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Quadratic Euler characteristic of symmetric powers of curves.

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Quadratic Euler characteristic of symmetric powers of curves.

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 that the power structure on the Grothendieck-Witt ring introduced by Pajwani-Pál computes the compactly supported $A^{1}$ -Euler characteristic of symmetric powers for all curves.

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来源期刊

Manuscripta Mathematica 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： manuscripta mathematica was founded in 1969 to provide a forum for the rapid communication of advances in mathematical research. Edited by an international board whose members represent a wide spectrum of research interests, manuscripta mathematica is now recognized as a leading source of information on the latest mathematical results.