Titlebook: Arithmetic and Geometry over Local Fields; VIASM 2018 Bruno Anglès,Tuan Ngo Dac Book 2021 Springer Nature Switzerland AG 2021 Differential

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,Difference Galois Theory for the “Applied” Mathematician,es, and we have devoted more space to statements useful in the applications. The applications concern many different mathematical settings, where linear difference equations naturally arise. We cite in particular the case of Drinfeld modules, which is considered in [Pel] and [TR].

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Berkovich Curves and Schottky Uniformization I: The Berkovich Affine Line,We define the Berkovich affine line and present its main properties, with many details: classification of points, path-connectedness, metric structure, variation of rational functions, etc. Contrary to many other introductory texts, we do not assume that the base field is algebraically closed.

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,Some Elements on Berthelot’s Arithmetic ,-Modules,ome finiteness properties of the constant coefficient which is constructed by adding overconvergent singularities. This lecture is suitable for graduate students and requires only basic knowledge of ring theory and algebraic geometry.

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Book 2021uthors, leading experts in the field, have put great effort into making the text as self-contained as possible, introducing the basic tools of the subject. The numerous concrete examples and suggested research problems will enable graduate students and young researchers to quickly reach the frontiers of this fascinating branch of mathematics..

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User Management and Database Securityome finiteness properties of the constant coefficient which is constructed by adding overconvergent singularities. This lecture is suitable for graduate students and requires only basic knowledge of ring theory and algebraic geometry.

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Expert Oracle Database Architecturea quotient of this kind. The guiding principle of our exposition is to stress notions and fully prove results in the theory of non-Archimedean curves that, to our knowledge, are not fully treated in other texts.

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Berkovich Curves and Schottky Uniformization II: Analytic Uniformization of Mumford Curves,a quotient of this kind. The guiding principle of our exposition is to stress notions and fully prove results in the theory of non-Archimedean curves that, to our knowledge, are not fully treated in other texts.

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