Alg??bre Locale, Multiplicit??s: Cours au Coll??ge de by Jean-Pierre Serre

By Jean-Pierre Serre

Chapitre I. 1DIAUX PIlEMIEIS IT LOCALISATION I I. Wotationa et definitions I 2. Lemme de Bakay. . . . 2 three. Localisation • • • four. Anneaux et 80dules noethiriens 2 five. Spectre•••••• three four 6. Le cas noetherien. four 7. Ideaux pre. iers associe. Chapitre eleven. OUTILS IT SOUTES A) Filtr·ations et graduations. eight I. Anneaux et modules filtres • eight 2. Topologie definie par UDe filtration nine 10 three. Coapletion des modules filtres • • • II four. Anneaux et modules graduis • • • • • five. au tout redevient noethirien; filtrations ~-adiques. 15 20 6. Modules differentiels filtres•••••••••••• B) Polynoaes de Hilbert-SamueL ••••••••••• 26 I. Rappel sur les polynOmes Ii valeurs entieres•••• 26 27 2. Fonctions ingredients sur les different types de modules. 29 three. Le polynOme caractiristique de Hilbert 32 four. Les invariants de Hilbert-Samuel Chapitre 111. T1I£ORlE DE los angeles DDlE!ISION A) size des extensions. entieres. 38 I. Definitions. • • • • • • • • • • • • 38 2. Le most popular theore- de Cohen-Seidenberg. 39 three. Le moment theoreme de Cohen-Seidenberg • 4I B) measurement dans les anneaux noetheriens. forty three I. measurement d'un module. • • • forty three 2. Le cas semi-local noetherien forty four three. Syste. es de parametres forty seven C) Anneaux normaux forty eight I. caracterisation des anneaux normaux. forty eight 2. Proprietes des anneaux noraaux fifty one three. Fermeture integrale. fifty three D) Anneaux de polynomes. • • • • • fifty four I.

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