Overview
Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 64)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This monograph is devoted to the problems of modules in scheme theory; the main purpose is to develop relative scheme theory over a ringed space. The exposition contains 8 chapters. Chapters I and II are devoted to the necessary information about 2-categories which simplifies the utilization of toposes. 2-category is a category in which the sets Hom are categories and where maps between Hom's have functorial nature. One studies U-toposes by means of this notion in chapter II, U being a fixed universimum. One introduces the notion of ringed U-toposand studies U-toposes ringed by local and strict local rings in chapter III. In the same chapter one solves the corresponding universal problem and as a result introduces the spectrum of ringed U-topos in chapter IV, what makes it possible to define the category of relative schemes over a ringed topos. In chapter V-VII the theory of relative S-schemes is developed where S is a ringed topos; then this theory applies to studying of the algebraic-analytic equivalence in chapter VIII. A. A. Bel'skii.
Authors and Affiliations
Bibliographic Information
Book Title: Topos anneles et schemas relatifs
Authors: Monique Hakim
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
DOI: https://doi.org/10.1007/978-3-662-59155-0
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 1972
Hardcover ISBN: 978-3-540-05573-0Published: 01 January 1972
eBook ISBN: 978-3-662-59155-0Published: 10 June 2019
Edition Number: 1
Number of Pages: VI, 162
Topics: Geometry