An Extension of the Galois Theory of Grothendieck PDF Download
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Author: André Joyal
Publisher: American Mathematical Soc.
ISBN: 0821823124
Category : Mathematics
Languages : en
Pages : 87
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Book Description
In this paper we compare, in a precise way, the concept of Grothendieck topos to the classical notion of topological space. The comparison takes the form of a two-fold extension of the idea of space.
Author: André Joyal
Publisher: American Mathematical Soc.
ISBN: 0821823124
Category : Mathematics
Languages : en
Pages : 87
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Book Description
In this paper we compare, in a precise way, the concept of Grothendieck topos to the classical notion of topological space. The comparison takes the form of a two-fold extension of the idea of space.
Author: Andre Joyal
Publisher:
ISBN: 9780608105116
Category :
Languages : en
Pages : 85
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Book Description
Author: Francis Borceux
Publisher: Cambridge University Press
ISBN: 9780521803090
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read.
Author: Jean-Pierre Serre
Publisher: CRC Press
ISBN: 1439865256
Category : Mathematics
Languages : en
Pages : 136
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Book Description
This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt constructi
Author: Tamás Szamuely
Publisher: Cambridge University Press
ISBN: 0521888506
Category : Mathematics
Languages : en
Pages : 281
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Book Description
Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Author: Emil Artin
Publisher:
ISBN: 9781950217021
Category : Education
Languages : en
Pages : 54
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Book Description
The author Emil Artin is known as one of the greatest mathematicians of the 20th century. He is regarded as a man who gave a modern outlook to Galois theory. Original lectures by the master. This emended edition is with completely new typesetting and corrections. The free PDF file available on the publisher's website www.bowwowpress.org
Author: Marius van der Put
Publisher: Springer Science & Business Media
ISBN: 3642557503
Category : Mathematics
Languages : en
Pages : 446
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Book Description
From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews
Author: 中村博昭
Publisher: Advanced Studies in Pure Mathe
ISBN: 9784864970143
Category : Mathematics
Languages : en
Pages : 0
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Book Description
From the 1980's, Grothendieck's "Esquisse d'un Programme" triggered tremendous developments in number theory and arithmetic geometry, extending from the studies of anabelian geometry and related Galois representations to those of polylogarithms and multiple zeta values, motives, rational points on arithmetic varieties, and effectiveness questions in arithmetic geometry. The present volume collects twenty-four articles written by speakers (and their coauthors) of two international meetings focused on the above themes held in Kyoto in October 2010. It includes both survey articles and research papers which provide useful information about this area of investigation.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America
Author: Barbara Fantechi
Publisher: American Mathematical Soc.
ISBN: 0821842455
Category : Mathematics
Languages : en
Pages : 354
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Book Description
Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.
Author: Pierre Colmez
Publisher: American Mathematical Society, Société Mathématique de France
ISBN: 1470469391
Category : Mathematics
Languages : en
Pages : 600
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Book Description
The book is a bilingual (French and English) edition of the mathematical correspondence between A. Grothendieck and J-P. Serre. The original French text of 84 letters is supplemented here by the English translation, with French text printed on the left-hand pages and the corresponding English text printed on the right-hand pages. The book also includes several facsimiles of original letters. The letters presented in the book were mainly written between 1955 and 1965. During this period, algebraic geometry went through a remarkable transformation, and Grothendieck and Serre were among central figures in this process. The reader can follow the creation of some of the most important notions of modern mathematics, like sheaf cohomology, schemes, Riemann-Roch type theorems, algebraic fundamental group, motives. The letters also reflect the mathematical and political atmosphere of this period (Bourbaki, Paris, Harvard, Princeton, war in Algeria, etc.). Also included are a few letters written between 1984 and 1987. The letters are supplemented by J-P. Serre's notes, which give explanations, corrections, and references further results. The book should be useful to specialists in algebraic geometry, in history of mathematics, and to all mathematicians who want to understand how great mathematics is created.
