Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/53106
Nombres $p$-àdics i mètodes local-globals
Journal Title
Authors
Director/Tutor
Journal ISSN
Volume Title
Related resource
Abstract
Originally, this project was motivated by the topological and analytical idea of completing a metric space through Cauchy sequences. More specifically, the curiosity came from a willing to study the result of (for a given prime number $p$) completing the set of rational numbers through the $p$-adic norm.
The object that arises from this completion of the rational number field is again a field, which we will call the field of the $p$-adic numbers, $\mathbb{Q}_p$. Although it can seem that $p$-adic numbers are an unnatural construction, their field has endless applications in number theory; a part from applications in algebra, topology, quantum mechanics, and complex dynamics. These fields could have many applications in other branches of science (not only in mathematics), which we still have to discover. Furthermore, $\mathbb{Q}_p$ is an object with its own mathematics, since it has been developed a theory of $p$-adic analysis, $p$-adic integration and, more recently, a still arising theory of $p$-adic dynamics.
Description
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2013, Director: Pilar Bayer i Isant
Subject (English)
Citation
Collections
Citation
CASASSAS MASSANA, Pau. Nombres $p$-àdics i mètodes local-globals. [consulted: 16 of June of 2026]. Available at: https://hdl.handle.net/2445/53106