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Table of contents

About this book

Introduction

From the reviews (Zentrallblatt MATH):

"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."

Keywords

Ring (Math.) Topos Grothendieck topologies scheme theory ringed space

Authors and affiliations

  1. 1.Université des Sciences et Techniques du LanguedocMontpellierFrance

Bibliographic information

  • Book Title Topos annelés et schémas 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
  • Copyright Information Springer-Verlag GmbH Germany, part of Springer Nature 1972
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-540-05573-0
  • eBook ISBN 978-3-662-59155-0
  • Edition Number 1
  • Number of Pages VI, 162
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Geometry
  • Buy this book on publisher's site