Open problems in the wild McKay correspondence and related fields

Abstract

The wild McKay correspondence is a form of McKay correspondence in terms of stringy invariants that is generalized to arbitrary characteristics. It gives rise to an interesting connection between the geometry of wild quotient varieties and arithmetic on extensions of local fields. The principal purpose of this article is to collect open problems on the wild McKay correspondence, as well as those in related fields that the author believes are interesting or important. It also serves as a survey on the present state of these fields.

20 pages

References in corpus (7)

• Densities of rational points and number fields
• Heights on stacks and a generalized Batyrev-Manin-Malle conjecture
• Crepant resolutions of quotient varieties in positive characteristics and their Euler characteristics
• Manin's conjecture vs. Malle's conjecture
• On Convergence of Stringy Motives of Wild $p^n$-Cyclic Quotient Singularities
• Wild Ramification and Restrictions to Curves
• The v-function in the wild McKay correspondence is not determined by the ramification filtration