Constructible motivic functions and motivic integration
By Raf Cluckers, François Loeser. 2004
176 citations recorded by the source corpus.
We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative framework, in which we develop a relative version of motivic integration. These results have been announced in math.AG/0403349 and math.AG/0403350. Main results and statements unchanged. Many minor slips corrected and some details added.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/bb8f18aceca476a3289089c85d59aa3fbe685df4
How researchers see this paper
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In Geometry and Topology
- Nicolas Templier
- Leonard Lipshitz
- S. Shin
- Raf Cluckers
- Peter Scholze
- T. Gee
- Thomas J. Haines
- J. Thorne
In Mathematical Physics
- Nicolas Templier
- Leonard Lipshitz
- S. Shin
- Raf Cluckers
- Peter Scholze
- T. Gee
- Thomas J. Haines
- J. Thorne
Citations in the corpus
- Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm (2005, unknown): “A u t h o r ' s p e r s o n a l”
- Sato–Tate theorem for families and low-lying zeros of automorphic $$L$$L-functions (2012, background): “Such a construction of measures associated with differential forms behaves well in the setting of motivic integrals because there exists a natural change of variables formula for motivic integrals, see §15 of [26].”
- Fields with analytic structure (2009, methodology): “In [ CL ], cell decomposition is used to dene motivic integrals; historically, cell decomposition has been used to calculate many types ofp-adic integrals [D1], [Pas1].”