Wilder McKay correspondences

Abstract

A conjectural generalization of the McKay correspondence in terms of stringy invariants to arbitrary characteristic, including the wild case, was recently formulated by the author in the case where the given finite group linearly acts on an affine space. In cases of very special groups and representations, the conjecture has been verified and related stringy invariants have been explicitly computed. In this paper, we try to generalize the conjecture and computations to more complicated situations such as non-linear actions on possibly singular spaces and non-permutation representations of non-abelian groups.

42 pages. The title has been changed from the previous "The motivic McKay correspondence for non-linear actions on possibly singular spaces". A new added subject is computations of weight functions and masses for some non-permutation representations. Comments are welcome

References in corpus (2)

• The wild McKay correspondence and $p$-adic measures
• Mass formulas for local Galois representations and quotient singularities II: dualities and resolution of singularities

Cited by in corpus (7)

• The wild McKay correspondence and $p$-adic measures
• Mass formulas for local Galois representations and quotient singularities II: dualities and resolution of singularities
• Inversion of adjunction for quotient singularities
• Motivic Zeta Functions on $\mathds{Q}$-Gorenstein Varieties
• Motivic integration over wild Deligne-Mumford stacks
• Motivic versions of mass formulas by Krasner, Serre and Bhargava
• Open problems in the wild McKay correspondence and related fields