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Topos annelés et schémas relatifs

  • Monique Hakim
Book

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge book series (MATHE2, volume 64)

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

  • Monique Hakim
    • 1
  1. 1.Université des Sciences et Techniques du LanguedocMontpellierFrance

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