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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LAVE

,Difference Galois Theory for the “Applied” Mathematician,e chosen to omit the proofs that are already presented in details in many references in the literature, although they were explained during the lectures, and we have devoted more space to statements useful in the applications. The applications concern many different mathematical settings, where line

噱頭

organic-matrix

DAMP

Berkovich Curves and Schottky Uniformization II: Analytic Uniformization of Mumford Curves,It is more advanced than the first part and covers the theory of Mumford curves and Schottky uniformization. We start by briefly reviewing the theory of Berkovich curves, then introduce Mumford curves in a purely analytic way (without using formal geometry). We define Schottky groups acting on the B

壁畫(huà)

On the Stark Units of Drinfeld Modules, of a Drinfeld module as defined by Taelman. We review some recent results on Drinfeld .-modules which make use of this notion. In particular, we present the “discrete Greenberg conjectures” which explain the structure of the class module of the canonical multi-variable deformations of the Carlitz m

玷污

可觸知

火海

Concurrency and Multi-Versioning,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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Concurrency and Multi-Versioning,ent the “discrete Greenberg conjectures” which explain the structure of the class module of the canonical multi-variable deformations of the Carlitz module, and a result on the non vanishing modulo a given prime of a class of Bernoulli-Carlitz numbers.