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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Uniform properties of rigid subanalytic sets


Authors: Leonard Lipshitz and Zachary Robinson
Journal: Trans. Amer. Math. Soc. 357 (2005), 4349-4377
MSC (2000): Primary 03C10, 32P05, 32B20; Secondary 26E30, 03C98
Published electronically: June 21, 2005
MathSciNet review: 2156714
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Abstract: In the context of rigid analytic spaces over a non-Archimedean valued field, a rigid subanalytic set is a Boolean combination of images of rigid analytic maps. We give an analytic quantifier elimination theorem for (complete) algebraically closed valued fields that is independent of the field; in particular, the analytic quantifier elimination is independent of the valued field's characteristic, residue field and value group, in close analogy to the algebraic case. This provides uniformity results about rigid subanalytic sets. We obtain uniform versions of smooth stratification for subanalytic sets and the \Lojasiewicz inequalities, as well as a unfiorm description of the closure of a rigid semianalytic set.


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Additional Information

Leonard Lipshitz
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: lipshitz@math.purdue.edu

Zachary Robinson
Affiliation: Department of Mathematics, East Carolina University, Greenville, North Carolina 27858
Email: robinsonz@mail.ecu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-05-04003-1
PII: S 0002-9947(05)04003-1
Received by editor(s): March 7, 2003
Published electronically: June 21, 2005
Additional Notes: This work was supported in part by NSF grant number DMS 0070724
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.