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Existential uniform p-adic integration and descent for integrability and largest poles
Multi angle
Authors : Cluckers, Raf (Author of the conference)
CIRM (Publisher )
03C98 - Applications of model theory
11F23 - Relations of number theory with algebraic geometry and topology
11S40 - Zeta functions and $L$-functions
11U09 - Model theory, See also {03Cxx}
14B05 - Singularities
14E18 - Arcs and motivic integration
CIRM (Publisher )
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Abstract :
I will report on work with Stout from arXiv:2304.12267. Since the work by Denef, p-adic cell decomposition provides a well-established method to study p-adic and motivic integrals. In this paper, we present a variant of this method that keeps track of existential quantifiers. This enables us to deduce descent properties for p-adic integrals. We will explain all this in the talk.
Keywords : Descent for integrability of p-adic integrals; cell decomposition; Igusa's local zeta functions; Serre-Poincaré series; log canonical threshold; oscillation index; semi-continuity of p-adic integrability indices
MSC Codes : Keywords : Descent for integrability of p-adic integrals; cell decomposition; Igusa's local zeta functions; Serre-Poincaré series; log canonical threshold; oscillation index; semi-continuity of p-adic integrability indices
03C98 - Applications of model theory
11F23 - Relations of number theory with algebraic geometry and topology
11S40 - Zeta functions and $L$-functions
11U09 - Model theory, See also {03Cxx}
14B05 - Singularities
14E18 - Arcs and motivic integration
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 23/06/2023 Conference Date : 01/06/2023 Subseries : Research talks arXiv category : Number Theory ; Algebraic Geometry ; Logic Mathematical Area(s) : Analysis and its Applications ; Algebraic & Complex Geometry ; Logic and Foundations ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:00:16 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-06-01_Cluckers.mp4 
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Information on the Event
Event Title : Model theory of valued fields / Théorie des modèles des corps valuésEvent Organizers : Chatzidakis, Zoé ; Jahnke, Franziska ; Rideau-Kikuchi, Silvain Dates : 29/05/2023 - 02/06/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2761.html
Citation Data
DOI : 10.24350/CIRM.V.20050603Cite this video as: Cluckers, Raf (2023). Existential uniform p-adic integration and descent for integrability and largest poles. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20050603 URI : http://dx.doi.org/10.24350/CIRM.V.20050603 |
See Also
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Bibliography
- CLUCKERS, Raf et STOUT, Mathias. Existential uniform $ p $-adic integration and descent for integrability and largest poles. arXiv preprint arXiv:2304.12267, 2023. - https://doi.org/10.48550/arXiv.2304.12267
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