Moduli of formal torsors II

Abstract

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 the wild McKay correspondence are well-defined.

arXiv comment36 pages, some improvements, accepted in Annales de l'Institut Fourier

References in corpus (5)

• The wild McKay correspondence and $p$-adic measures
• Mass formulas for local Galois representations and quotient singularities I: a comparison of counting functions
• Toward motivic integration over wild Deligne-Mumford stacks
• Mass formulas for local Galois representations and quotient singularities II: dualities and resolution of singularities
• Algebraic and Nori fundamental gerbes

Cited by in corpus (3)

• Motivic integration over wild Deligne-Mumford stacks
• The v-function in the wild McKay correspondence is not determined by the ramification filtration
• Motivic versions of mass formulas by Krasner, Serre and Bhargava