Algebra and Galois Theories

Régine , Douady-Adrien , Douady


anglais | 14-07-2021 | 488 pages

9783030327989

Livre de poche


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Couverture / Jaquette

Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.

Note biographique

Adrien DOUADY was born in 1935. After receiving his Ph.d. in mathematics in the field of complex analytic geometry, he later joined the University Paris-Sud (Orsay). A recipient of the Ampere prize, he was a member of the French Academy of Sciences, as well as of the highly influential informal Bourbaki group. Throughout his life, he remained interested in several areas. Yet his odyssey always brought back to complex numbers. He passed away in 2006, and is notably survived by his wife, Regine Douady. 


Regine Douady, born in 1934,  after a Ph.d. in the didactics of mathematics, she became a lecturer at the University Paris Denis-Diderot, as well as the head of the IREM (Institut de Recherche sur l' Enseignement des Mathematiques). She was made a chevalier dans l'ordre des palmes academiques. Now retired, she has ceaselessly endeavoured to introduce into teaching the necessity to address concepts from different standpoints-the motivating idea behind this book.

Fonctionnalité

This book aims to transfer geometric intuition to the algebraic framework of Galois theory

Gives a parallel presentation of Galois theory and the theory of covering spaces and highlights this similarity between the two

Useful both for undergraduates and graduates, as well as to any researcher wishing to go beyond a purely algebraic approach to Galois theory

Table des matières

Introduction.- Chapter 1. Zorn's Lemma.- Chapter 2. Categories and Functors.- Chapter 3. Linear Algebra.- Chapter 4. Coverings.- Chapter 5. Galois Theory.- Chapter 6. Riemann Surfaces.- Chapter 7. Dessins d'Enfants.- Bibliography.- Index of Notation

Détails

Code EAN :9783030327989
Auteur(trice): 
Editeur :Springer International Publishing-Springer International Publishing-Springer International Publishing
Traduit par : Urmie , Ray
Date de publication :  14-07-2021
Format :Livre de poche
Langue(s) : anglais
Hauteur :235 mm
Largeur :155 mm
Epaisseur :27 mm
Poids :733 gr
Stock :Impression à la demande (POD)
Nombre de pages :488
Mots clés :  Coverings fundamental group (mappings); Curves; Galois theory; Separable Extensions; fundamental groups; homotopy theory