Journal article
Uniform parameterization of subanalytic sets and diophantine applications
- Abstract:
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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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- Files:
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(Accepted manuscript, pdf, 691.3KB)
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- Publisher copy:
- 10.24033/asens.2416
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Authors
Funding
French National Research Agency
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Bibliographic Details
- 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:
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1873-2151
- ISSN:
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0012-9593
- Source identifiers:
-
846016
Item Description
- Language:
- English
- Keywords:
- Pubs id:
-
pubs:846016
- UUID:
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uuid:21ec8d7e-6c15-48a2-b845-362a45725cd8
- Local pid:
- pubs:846016
- Deposit date:
- 2018-05-04
Terms of use
- Copyright holder:
- Société Mathématique de France
- Copyright date:
- 2020
- Rights statement:
- © 2020 Société Mathématique de France, Paris
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Société Mathématique de France at https://doi.org/10.24033/asens.2416
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