Résidus et dualité : prénotes pour un 'Séminaire Hartshorne' / Alexandre Grothendieck ; édité par Robin Hartshorne.

Format:

Book

Author/Creator:

Grothendieck, A. (Alexandre)

Contributor:

Hartshorne, Robin, editor, writer of introduction.

Series:

Documents mathématiques ; 21.

Documents mathématiques, 1629-4939 ; 21

Language:

French

Subjects (All):

Geometry, Algebraic.

Duality theory (Mathematics).

Categories (Mathematics).

Physical Description:

xxiv, 165 pages : some illustrations, facsimile ; 25 cm

Place of Publication:

Paris, France : Société Mathématique de France, 2024.

Language Note:

Text in French with preface and Introduction to prénotes in English.

Summary:

"In the fall of 1963, there was a seminar at Harvard on duality theorems in algebraic geometry. The seminar's aim was to understand how the systematic use of the revolutionary new method of derived categories had enabled Grothendieck to generalize to the relative case, for a proper morphism of schemes, the duality theorems of Serre for projective varieties over a field. Presented here are the typewritten "prenotes" which Grothendieck prepared to guide Hartshorne in running the seminar. Unpublished until now, they show the mathematician as he reached the height of his creative powers.This edition also contains a preface by Hartshorne explaining the origins of the ideas presented in the seminar, together with a discussion of the differences between these prenotes and his report in the Springer Lecture Notes Residues and Duality of 1966, where the derived category and these new duality theorems appeared for the first time in print."- publisher

Contents:

Preface

Introduction to prénotes / by Robin Hartshorne

Appendix. Material in Prénotes not discussed in [11]

Bibliography

Commentaires

Notations

Catégories dérivées. Quelques résultats

Le théorème de dualité pour f :Pn S -> S

Le théorème de dualité pour les morphismes simples et propres

Théorie homotopique des résidus et théorème de dualité pour un morphisme propre : énoncés

La variance f! pour les pseudo-complexes et théorie locale des résidus. Applications : modules fondamentaux relatifs, théorie de la différente

Compléments au chapitre 5

Cohomologie locale et résolutions canoniques

Complexes résiduels et bidualité

Applications à la dualité globale.

Notes:

Includes bibliographical references (pages xxiii-xxiv).

ISBN:

9782856299838

2856299830

OCLC:

1463353020