We study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick tensor subcategory of Voevodsky’s triangulated category of motives with rational coefficients generated by the motive of C. Moreover, over a field of characteristic zero, we prove a motivic non-abelian Hodge correspondence: the integral motives of the Higgs and de Rham moduli spaces are isomorphic.

中文翻译：

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关于曲线上希格斯束模空间的Voevodsky动机

我们假设C有一个合理的点，研究场k上光滑投影曲线C上的互质秩和度的半稳定希格斯束的模空间的动机。我们表明，该动机包含在Voevodsky三角剖分动机类别的厚张量子类别中，该动机由C动机生成有理系数。此外，在特征为零的域上，我们证明了一个动机非阿贝尔霍奇对应：希格斯模和de Rham模空间的积分动机是同构的。