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Master thesis

Publication date

2024-06-04

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cc by-nc-nd (c) Oriol Reig Fité, 2024
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/216960

Introduction to Berkovich spaces

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Abstract

In this Master Final Project I have studied Berkovich spaces, which is one of the existing approaches to non-Archimedean geometry, a branch that deals with analytic spaces over non-Archimedean fields. Let us first give some context on $p$-adic geometry and the necessity to develop such a theory of analytic spaces. Any norm gives rise to a metric space by setting the distance between two elements as the norm of their difference. In the case of a metric space induced by a non-Archimedean norm, the topological space is totally disconnected. For this reason, when we try to develop a theory of analytic functions similar that for the complex case (i.e., the Archimedean case), we encounter some notorious problems.

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Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Martín Sombra

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Anàlisi p-àdica, Espais topològics, Treballs de fi de màster, Espais analítics

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p-adic analysis, Topological spaces, Master's thesis, Analytic spaces

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Màster Oficial - Matemàtica Avançada

Citation

REIG FITÉ, Oriol. Introduction to Berkovich spaces. [consulted: 7 of June of 2026]. Available at: https://hdl.handle.net/2445/216960

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