Cell decomposition and p-adic integration
| dc.creator | Cluckers, Raf | |
| dc.date | 2003-01-03 | |
| dc.date.accessioned | 2026-07-07T04:54:15Z | |
| dc.date.available | 2026-07-07T04:54:15Z | |
| dc.description | A semialgebraic bijection from the field of p-adic numbers to itself minus one point is constructed. Semialgebraic p-adic sets are classified up to semialgebraic bijection. A cell decomposition theorem for restricted analytic p-adic maps is proven, in analogy with the cell decomposition theorem for polynomial maps by Denef. This cell decomposition is used to show that a certain algebra (built up with analytic and subanalytic p-adic functions) is closed under p-adic integration. This solves a conjecture of Denef on parametrized analytic p-adic integrals. Local (analytic) singular series are shown to be in this algebra. Subanalytic p-adic sets are classified up to subanalytic bijection. Multivariate Kloosterman sums are studied modulo powers of p. A qualitative decay rate is obtained when this power goes to infinity. This is a multivariate analogue of a result of Igusa's. Also Presburger groups are studied. A dimension for Presburger sets is defined, Presburger sets are classified up to definable bijection, and elimination of imaginaries is proven. Grothendieck rings of several classes of valued fields are calculated. | |
| dc.description | Thesis made under supervision of Prof. dr. J. Denef, defended on december 18 2002 at KULeuven, Belgium | |
| dc.identifier | https://arxiv.org/abs/math/0301023 | |
| dc.identifier | http://arxiv.org/abs/math/0301023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66174 | |
| dc.subject | Logic | |
| dc.subject | Number Theory | |
| dc.subject | 03C98, 11S80, 11S40, 03C10, 11U09, 03C07, 03C60, 12L12 | |
| dc.title | Cell decomposition and p-adic integration | |
| dc.type | text |