Motivic integration in all residue field characteristics for Henselian discretely valued fields of characteristic zero
-
Raf Cluckers
and
François Loeser
Abstract
We extend the formalism and results on motivic integration from [Invent. Math. 173 (2008), 23–121] to mixed characteristic discretely valued Henselian fields with bounded ramification. We also generalize the equicharacteristic zero case of loc. cit. by giving, in all residue characteristics, an axiomatic approach (instead of only using Denef–Pas languages) and by using richer angular component maps. In this setting we prove a general change of variables formula and a general Fubini Theorem. Our set-up can be specialized to previously known versions of motivic integration by e.g. the second author and J. Sebag and to classical p-adic integrals.
Funding source: European Research Council
Award Identifier / Grant number: European Community's Seventh Framework Programme (FP7/2007–2013)/ERC Grant Agreement no. 246903 NMNAG
Funding source: Fund for Scientific Research – Flanders
Award Identifier / Grant number: G.0415.10
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Motivic integration in all residue field characteristics for Henselian discretely valued fields of characteristic zero
- A Satake isomorphism for representations modulo p of reductive groups over local fields
- Quantum Grothendieck rings and derived Hall algebras
- On Lagrangian fibrations by Jacobians I
- From exceptional collections to motivic decompositions via noncommutative motives
- Branched Willmore spheres
- Mori dream spaces of Calabi–Yau type and log canonicity of Cox rings
- On inductively free reflection arrangements
- Willmore surfaces in 3-sphere foliated by circles
Articles in the same Issue
- Frontmatter
- Motivic integration in all residue field characteristics for Henselian discretely valued fields of characteristic zero
- A Satake isomorphism for representations modulo p of reductive groups over local fields
- Quantum Grothendieck rings and derived Hall algebras
- On Lagrangian fibrations by Jacobians I
- From exceptional collections to motivic decompositions via noncommutative motives
- Branched Willmore spheres
- Mori dream spaces of Calabi–Yau type and log canonicity of Cox rings
- On inductively free reflection arrangements
- Willmore surfaces in 3-sphere foliated by circles
