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.

arXiv comment20 pages

References in corpus (18)

• Stringy Hodge numbers of varieties with Gorenstein canonical singularities
• Twisted jets, motivic measure and orbifold cohomology
• On the distribution of Galois groups
• Tamagawa numbers of polarized algebraic varieties
• Motivic integration, quotient singularities and the McKay correspondence
• The wild McKay correspondence and $p$-adic measures
• Mass formulas for local Galois representations and quotient singularities I: a comparison of counting functions
• Wilder McKay correspondences
• Mass formulas for local Galois representations and quotient singularities II: dualities and resolution of singularities
• Cohomological Hasse principle and resolution of quotient singularities
• The Wild McKay Correspondence for Cyclic Groups of Prime Power Order
• Heights on stacks and a generalized Batyrev-Manin-Malle conjecture
• Densities of rational points and number fields
• 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
• The v-function in the wild McKay correspondence is not determined by the ramification filtration
• Wild Ramification and Restrictions to Curves