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Reduction modulo pn of p-adic subanalytic sets

Published online by Cambridge University Press:  24 October 2008

Willem Veys
Affiliation:
K. U. Leuven, Departement Wiskunde, Celestijnenlaan 200-B, B-3001 Leuven, Belgium

Extract

Let ℚp and ℤp respectively denote the p-adic numbers and the p-adic integers for a fixed prime number p. For any subset Y of and n ∈ ℕ we denote by Nn(Y) the cardinality of the image of Y under the natural map . (Thus we have Nn(Y)≤ pnr.)

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

[1]Bourbaki, N.. Variétés Différentielles et Analytiques. Fascicule de Résultats (Hermann, 1967).Google Scholar
[2]Denef, J.. Multiplicity of the poles of the Poincaré series of a p-adic subanalytic set. Séminaire de Théorie des Nombres de Bordeaux (19871988), 43/01–43/08.Google Scholar
[3]Denef, J. and Van Den Dries, L.. p-adic and real subanalytic sets. Ann. of Math. (2) 128 (1988), 79138.CrossRefGoogle Scholar
[4]Oesterlé, J.. Réduction modulo p n des sous-ensembles analytiques fermés de . Invent. Math. 66 (1982), 325341.CrossRefGoogle Scholar
[5]Serre, J.-P.. Quelques applications du théorème de densité de Chebotarev. Inst. Hautes Études Sci. Publ. Math. 54 (1981), 123201.CrossRefGoogle Scholar