Parameterized stratification and piece number of D-semianalytic sets
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Y. Firat Çelikler
Abstract
We obtain results on the geometry of D-semianalytic and subanalytic sets over a complete, non-trivially valued non-Archimedean field K, which is not necessarily algebraically closed. Among the results are the Parameterized Smooth Stratification Theorem and several results concerning the dimension theory of D-semianalytic and subanalytic sets. Also, an extension of Bartenwerfer's definition of piece number for analytic K-varieties is provided for the D-semianalytic sets and the existence of a uniform bound for the piece number of the fibers of a D-semianalytic set is proved. There is a connection between the piece number and the complexity of a D-semianalytic set which is a subset of the affinoid line and therefore a simpler proof of the Complexity Theorem of Lipshitz and Robinson is made possible by these results. Finally we prove an analogue of a theorem by van den Dries, Haskell and Macpherson, which states that for each D-semianalytic X, there is a semialgebraic Y such that one dimensional fibers of X are among the one dimensional fibers of Y through an easy application of our earlier results.
© Walter de Gruyter
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Articles in the same Issue
- Parabolic equations with BMO nonlinearity in Reifenberg domains
- Castelnuovo theory and the geometric Schottky problem
- Cohomology of rational forms and a vanishing theorem on toric varieties
- On the asymptotic expansion of complete Ricciflat Kähler metrics on quasi-projective manifolds
-
The Chow ring of
- Explicit n-descent on elliptic curves, I. Algebra
- On the Lp-Lq maximal regularity of the Neumann problem for the Stokes equations in a bounded domain
- Parameterized stratification and piece number of D-semianalytic sets
