Geodesic
Overconvergent subanalytic subsets in the framework of Berkovich spaces
Journal of the European Mathematical Society, Tome 18 (2016) no. 10, pp. 2405-2457

Voir la notice de l'article provenant de la source EMS Press

We study the class of overconvergent subanalytic subsets of a k-affinoid space X when k is a non-archimedean field. These are the images along the projection X×Bn→X of subsets defined with inequalities between functions of X×Bn which are overconvergent in the variables of Bn. In particular, we study the local nature, with respect to X, of overconvergent subanalytic subsets. We show that they behave well with respect to the Berkovich topology, but not to the G-topology. This gives counter-examples to previous results on the subject, and a way to correct them. Moreover, we study the case dim(X)=2, for which a simpler characterisation of overconvergent subanalytic subsets is proven.
DOI : 10.4171/jems/643
Classification : 14-XX, 03-XX, 12-XX, 32-XX
Keywords: Berkovich spaces, semianalytic sets, subanalytic sets, overconvergent 
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     author = {Florent Martin},
     title = {Overconvergent subanalytic subsets in the framework of {Berkovich} spaces},
     journal = {Journal of the European Mathematical Society},
     pages = {2405--2457},
     publisher = {mathdoc},
     volume = {18},
     number = {10},
     year = {2016},
     doi = {10.4171/jems/643},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/643/}
}
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Florent Martin. Overconvergent subanalytic subsets in the framework of Berkovich spaces. Journal of the European Mathematical Society, Tome 18 (2016) no. 10, pp. 2405-2457. doi: 10.4171/jems/643

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