Moduli of formal torsors II
Annales de l'Institut Fourier, Online first, 48 p.

Applying the authors’ preceding work, we construct a version of the moduli space of G-torsors over the formal punctured disk for a finite group G. To do so, we introduce two Grothendieck topologies, the sur (surjective) and luin (locally universally injective) topologies, and define P-schemes using them as variants of schemes. Our moduli space is defined as a P-scheme approximating the relevant moduli functor. We then prove that Fröhlich’s module resolvent gives a locally constructible function on this moduli space, which implies that motivic integrals appearing in the wild McKay correspondence are well-defined.

En appliquant le travail précédent des auteurs, nous construisons une version d’un espace de modules de G-torseurs sur le disque perforé formel pour un groupe fini G. Dans ce but, nous introduisons deux topologies de Grothendieck, les topologies sur (surjective) et luin (localement universellement injective), et définissons des P-schémas en les utilisant comme variantes de schémas. Notre espace de modules est défini comme un P-schéma approximant le foncteur de modules pertinent. On montre alors que la résolvante de modules de Fröhlich donne une fonction localement constructible sur cet espace de modules, ce qui implique que les intégraux motiviques apparaissant dans la correspondance sauvage de McKay sont bien définis.

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Accepted:
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DOI: 10.5802/aif.3533
Classification: 14D22,  13F25,  14H30
Keywords: Moduli space, Grothendieck topologies, torsors, motivic integration, the wild McKay correspondence, Fröhlich’s module resolvent.
Tonini, Fabio 1; Yasuda, Takehiko 2

1 Universitá degli Studi di Firenze Dipartimento di Matematica e Informatica ‘Ulisse Dini’ Viale Giovanni Battista Morgagni, 67/A 50134 Firenze (Italy)
2 Department of Mathematics Graduate School of Science Osaka University Toyonaka, Osaka 560-0043 (Japan)
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Tonini, Fabio; Yasuda, Takehiko. Moduli of formal torsors II. Annales de l'Institut Fourier, Online first, 48 p.

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