Get Algèbre commutative: Chapitre 10 PDF

By N. Bourbaki

ISBN-10: 3540343946

ISBN-13: 9783540343943

ISBN-10: 3540343954

ISBN-13: 9783540343950

Algèbre commutative, Chapitre 10

Profondeur, régularité, dualité

Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements.

Ce quantity du Livre d’Algèbre commutative, septième Livre du traité, est los angeles continuation des chapitres antérieurs. Il introduit notamment les notions de profondeur et de lissité, fondamentales en géometrie algébrique. Il se termine par l’introduction des modules dualisants et de los angeles dualité de Grothendieck.

Ce quantity est paru en 1998.

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Extra resources for Algèbre commutative: Chapitre 10

Sample text

7. Anneaux de Gorenstein D ~ F I N I T I O1N . l:on, ~L(L~~~TIm I , ( Lde ~ A. u

X t A ( ~ ~ , Aest ) nul pour. i < (1, l ' a r ~ i ~ c A 11" 3, prop 3) ; si l'ürirlcai* A est tlc: Mami~liiy,la, suitc x est A-rCguliGrc (loc. , th. 1) ; si la suite x est A-régidiére, on a EX~;(K*,A) = O poi1r 1: < il et, les K*-espaces vectoriels E X ~ ~ ( K ~et, IAf o) ~ r i , ~ ( ~ ~ , A sont / x )isorrioipkies (A, X, p. 166, prop. 9). Cela prouve l'équiwlence des corrditioris (iv). (v) et (vi). Proilvons que (i) irnpliqiie (v) : si A rst. lin anneau de Corenstrin, c'est lin anneail de ICIaca,ulüy (prop.

La suite x est alors A-régulière (5 2, r1° 3, prop. 4): d o r ~ A/x est. cc vectoriel H o m A ( ~ *A, l r ) est, de diniension 1 . il d~ Gorcnst-cin (c~xcnlplc3). Ccla r6siiltc t h th. 2 si A est lin imilcail tlc Gorcnstcii~ct clil lcrn~ncs2 siiloii. rrt,d Ext:,,,, (A/m, A,) = O . 111 de A, il eziste un ent%er ;, > ht(m) tel grre (i) + (ii) : cela rCsliltc clil th. à l'anncnii local dc Gorciistciii Ap (exemple 1). (ii) + (iii) : c'est Lrivial. (iii) + (i) : sous l'hypotl~iw(iii), A,,, cst 1111 anuciiu de Gortwstcin pour tou1 idéal maximal m de A (th.

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Algèbre commutative: Chapitre 10 by N. Bourbaki


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