Toward motivic integration over wild Deligne-Mumford stacks

Abstract

We discuss how the motivic integration will be generalized to wild Deligne-Mumford stacks, that is, stabilizers may have order divisible by the characteristic of the base or residue field. We pose several conjectures on this topic. We also present some possible applications concerning stringy invariants, resolution of singularities, and weighted counts of extensions of local fields.

24 pages; minor corrections, added footnotes to mention subsequent developments, to appear in the proceedings of the conference "Higher Dimensional Algebraic Geometry - in honour of Professor Yujiro Kawamata's sixtieth birthday" (ASPM)

References in corpus (7)

• The $p$-cyclic McKay correspondence via motivic integration
• 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
• Stacks of ramified Galois covers

Cited by in corpus (9)

• Mass formulas for local Galois representations and quotient singularities I: a comparison of counting functions
• The wild McKay correspondence and $p$-adic measures
• Mass formulas for local Galois representations and quotient singularities II: dualities and resolution of singularities
• Modular quotient varieties and singularities by the cyclic group of order $2p$
• The Wild McKay Correspondence for Cyclic Groups of Prime Power Order
• Moduli of formal torsors II
• Motivic integration over wild Deligne-Mumford stacks
• Euler characteristic of crepant resolutions of specific modular quotient singularities
• Moduli of formal torsors