Smooth points of \(p\)-adic subanalytic sets
type: Item
instance of: scholarly article
title: Smooth points of \(p\)-adic subanalytic sets
zbMATH Open document ID: 0803.14010
DOI: 10.1007/BF03026536
author: Zachary Robinson
published in: Manuscripta Mathematica
publication date: 1994-12-15T00:00:00Z
full work available at URL: https://eudml.org/doc/155858
review text: The author proves some results on the singular locus of a subanalytic subset of \(\mathbb{Z}_ p^ m\). These results extend to the \(p\)-adic fields real variables theorems by \textit{M. Tamm}. The main results are the following: (1) the singular locus of a subanalytic set is itself subanalytic. (2) if \(f\) is a subanalytic function with domain contained in \(\mathbb{Z}_ p^ m\), then there exists an integer \(L\) such that for any point \(x_ 0 \in \mathbb{Z}^ m_ p\) in a neighborhood of which \(f\) is defined, \(f\) is strongly differentiable up to order \(L\) at \(x_ 0\) if, and only if \(f\) is analytic around \(x_ 0\).
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 32B20
zbMATH DE Number: 492806
zbMATH Keywords: singular locus of a subanalytic set
reviewed by: Guido Van Steen
MaRDI profile type: Publication
cites work: Die Beschränktheit der Stückzahl der Fasern K-analytischer Abbildungen.
cites work: Differentialrechnung in der analytischen Geometrie
cites work: Semianalytic and subanalytic sets
cites work: Q3325851
cites work: Q3963102
cites work: \(p\)-adic and real subanalytic sets
cites work: A full uniform Artin-Rees theorem.
cites work: Géométrie analytique rigide et applications. (Ridgid analytic geometry and applications)
cites work: Projections of semi-analytic sets
cites work: FORMAL RELATIONS BETWEEN ANALYTIC FUNCTIONS
cites work: Stratification of real analytic mappings and images
cites work: Q4050890
cites work: Q3775657
cites work: Rigid Subanalytic Sets
cites work: Q5651510
cites work: Frobenius avec singularites. II: Le cas général
cites work: Q3992979
cites work: Q3346515
cites work: Lie algebras and Lie groups. 1964 lectures, given at Harvard University.
cites work: Subanalytic sets in the calculus of variation
OpenAlex ID: W2023548227
description: scientific article; zbMATH DE number 492806