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Uniform parameterization of subanalytic sets and diophantine applications

Abstract:

We prove new parameterization theorems for sets definable in the structure Ran (i.e., for globally subanalytic sets) which are uniform for definable families of such sets. We treat both Cr-parameterization and (mild) analytic parameterization. In the former case we establish a polynomial (in r) bound (depending only on the given family) for the number of parameterizing functions. However, since uniformity is impossible in the latter case (as was shown by Yomdin via a very simple family of alg...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.24033/asens.2416

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Wolfson College
Role:
Author
ORCID:
0000-0003-3958-2338
More by this author
Institution:
University of Oxford
Department:
Mathematical Institute
Role:
Author
French National Research Agency More from this funder
Publisher:
Société Mathématique de France Publisher's website
Journal:
Annales Scientifiques de l'École Normale Supérieure Journal website
Volume:
53
Issue:
1
Pages:
1-42
Publication date:
2020-04-23
Acceptance date:
2018-04-20
DOI:
EISSN:
1873-2151
ISSN:
0012-9593
Source identifiers:
846016

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