[Modules de torseurs formels II]
En appliquant le travail précédent des auteurs, nous construisons une version d’un espace de modules de -torseurs sur le disque perforé formel pour un groupe fini . 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.
Applying the authors’ preceding work, we construct a version of the moduli space of -torsors over the formal punctured disk for a finite group . 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.
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Keywords: Moduli space, Grothendieck topologies, torsors, motivic integration, the wild McKay correspondence, Fröhlich’s module resolvent.
Mot clés : Espace de modules, topologies de Grothendieck, torseurs, intégration motivique, correspondance sauvage de McKay, résolvante de modules de Fröhlich.
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@article{AIF_2023__73_2_511_0,
author = {Tonini, Fabio and Yasuda, Takehiko},
title = {Moduli of formal torsors {II}},
journal = {Annales de l'Institut Fourier},
pages = {511--558},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {73},
number = {2},
year = {2023},
doi = {10.5802/aif.3533},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3533/}
}
TY - JOUR AU - Tonini, Fabio AU - Yasuda, Takehiko TI - Moduli of formal torsors II JO - Annales de l'Institut Fourier PY - 2023 SP - 511 EP - 558 VL - 73 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3533/ DO - 10.5802/aif.3533 LA - en ID - AIF_2023__73_2_511_0 ER -
%0 Journal Article %A Tonini, Fabio %A Yasuda, Takehiko %T Moduli of formal torsors II %J Annales de l'Institut Fourier %D 2023 %P 511-558 %V 73 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3533/ %R 10.5802/aif.3533 %G en %F AIF_2023__73_2_511_0
Tonini, Fabio; Yasuda, Takehiko. Moduli of formal torsors II. Annales de l'Institut Fourier, Tome 73 (2023) no. 2, pp. 511-558. doi : 10.5802/aif.3533. https://aif.centre-mersenne.org/articles/10.5802/aif.3533/
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