On the Voevodsky motive of the moduli space of Higgs bundles on a curve

Victoria Hoskins ^[1] ; Simon Pepin Lehalleur ^[1]
1. [1] Radboud University, Países Bajos
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 1, 2021
Idioma: inglés
DOI: 10.1007/s00029-020-00610-5
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Resumen
- 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.