Douady, Régine. creator author. aut http://id.loc.gov/vocabulary/relators/aut Douady, Adrien. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text gw 2020 1st ed. 2020. monographic eng

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access XXIII, 462 p. 33 illus., 6 illus. in color. online resource. 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. 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. by Régine Douady, Adrien Douady. Algebra Algebra QA150-272 512 9783030327965 https://doi.org/10.1007/978-3-030-32796-5 https://doi.org/10.1007/978-3-030-32796-5 200713 20200904104947.0 978-3-030-32796-5