Algebre Locale Multiplicites : Cours Au College D

P. Gabriel

Algebre Locale Multiplicites : Cours Au College D
Format
Paperback
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Country
Germany
Published
21 February 1975
Pages
176
ISBN
9783540070283

Algebre Locale Multiplicites : Cours Au College D

P. Gabriel

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Chapitre I. 1DIAUX PIlEMIEIS IT LOCALISATION I I. Wotationa et definitions I 2. Lemme de Bakay… . 2 3. Localisation - - - 4. Anneaux et 80dules noethiriens 2 5. Spectre—— 3 4 6. Le cas noetherien. 4 7. Ideaux pre. iers associe. Chapitre 11. OUTILS IT SOUTES A) Filtr-ations et graduations. 8 I. Anneaux et modules filtres - 8 2. Topologie definie par UDe filtration 9 10 3. Coapletion des modules filtres - - - II 4. Anneaux et modules graduis - - - - - 5. 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 additives sur les categories de modules. 29 3. Le polynOme caractiristique de Hilbert 32 4. Les invariants de Hilbert-Samuel Chapitre 111. T1IGBPORlE DE LA DDlE!ISION A) Dimension des extensions. entieres. 38 I. Definitions. - - - - - - - - - - - - 38 2. Le premier theore- de Cohen-Seidenberg. 39 3. Le second theoreme de Cohen-Seidenberg - 4I B) Dimension dans les anneaux noetheriens. 43 I. Dimension d'un module. - - - 43 2. Le cas semi-local noetherien 44 3. Syste. es de parametres 47 C) Anneaux normaux 48 I. caracterisation des anneaux normaux. 48 2. Proprietes des anneaux noraaux 51 3. Fermeture integrale. 53 D) Anneaux de polynomes. - - - - - 54 I.

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