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- W188045191 abstract "Nous d'emontrons un th'eor`eme de division de Weierstrass pour les points rigides des fibres d'un espace de Berkovich affine X sur un anneau de Banach A et en tirons des informations sur la structure locale de X. Lorsque A est un corps valu'e complet, un anneau de valuation discr`ete ou un anneau d'entiers de corps de nombres, nous en d'eduisons qu'en tout point de X, la fibre du faisceau structural est un anneau local noeth'erien et r'egulier. Nous montrons 'egalement que le faisceau structural est coh'erent. Nos m'ethodes traitent de fac{c}on unifi'ee espaces complexes et p-adiques. Weierstrass division theorem over a Banach ring. Application to Berkovich spaces over Z. We prove a Weierstrass division theorem for the rigid points of the fibers of an affine Berkovich space X over a Banach ring A and use it to study the local structure of X. In case A is a valued field, a discrete valuation ring or the ring of integers of a number field, we deduce that the stalks of the structure sheaf of X are noetherian and regular local rings. We also prove that the structure sheaf is coherent. Our methods provide a unified treatment of complex and p-adic spaces." @default.
- W188045191 created "2016-06-24" @default.
- W188045191 creator A5046157582 @default.
- W188045191 date "2012-02-03" @default.
- W188045191 modified "2023-09-27" @default.
- W188045191 title "Th'eor`eme de division de Weierstrass sur un anneau de Banach. Application aux espaces de Berkovich sur Z" @default.
- W188045191 hasPublicationYear "2012" @default.
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