Get Algèbre locale, multiplicités PDF

By Jean-Pierre Serre, Pierre Gabriel

ISBN-10: 3540070281

ISBN-13: 9783540070283

This variation reproduces the second corrected printing of the 3rd variation of the now vintage notes through Professor Serre, lengthy demonstrated as one of many commonplace introductory texts on neighborhood algebra. Referring for heritage notions to Bourbaki's "Commutative Algebra" (English version Springer-Verlag 1988), the publication focusses at the a number of size theories and theorems on mulitplicities of intersections with the Cartan-Eilenberg functor Tor because the relevant idea. the most effects are the decomposition theorems, theorems of Cohen-Seidenberg, the normalisation of jewelry of polynomials, measurement (in the feel of Krull) and attribute polynomials (in the experience of Hilbert-Samuel).

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Additional info for Algèbre locale, multiplicités

Example text

La vari~t~ associ@e au module nul est vide. I)~----~2): En effet, ceci est v~ai si au corps des fractions de ~ = A/p (alors d'oG M contient un sous-module 0--~ Np ~Mp et comme _ Enfin, si pest p associ@ ~ on tire donc M N p isomorphe ~ N # 0 est associ~ ~ A/p , on a bien =~= 0 M P ; de . ~p ~ (~/P)p-~ M , ; ~ 0 . P est premier essentiel d'un sous-module M/P s'identifie p A/p ). x ~ 0 A - ~ pour tout s~ 0 , il existe et 3)~--~4): D@j~ vu . 4)~I): Supposons en effet que associ@ ~ M A/~ , et . Alors N Cor~llaire: N' est associ~ ~ dans M Si p~V(M) 0 = M ~~ M I C .

I et a. ,V(M4) J S. = A - ~ 3 ~j,k j/i M Comme, pour i ' ~i,e / j V(Mj) = W(a_j) ~i,e , aucun , oG d@signent les id@aux pre- et appartenant rencontre t o u s l e s de 0 M Di, e ~ et donc aussi contient alors M. ,Pj,tj miers associ@s & ~j,k 9 J 1~kQt i, j ~ s M1 , M2 , : Soit en effet 1~ d@termine et coupe a. La 9 ---i N. -composante l suivant 0 . l (M/o) R=~ci_pro~uement= a. --l M 1 N 9149 , sont @trangers deux & deux. Soit alors Alors ,. supposons donn@e une d@composition a=~l o~ les -- b. + ,~9.

A-module de t~pe fini est s@par@ pour la topolo~ie ~-adi~ue. (iii) Tout sous-module d'un A-module de type fini est ferm@ pour la topologie ~-adi~ue. (i) de - )(ii). P ceci entra~ne (ii) ~(iii). l'adh@rence P = 0 Si N de z@ro; la topologie )(i). ferm@ dans A Corollaire ~: q n Soit m N A et comme de M , le fait que soit ferm@. P q-adique (lemme de Nakayama). est un sous-module soit s@par@ entraSne que (iii) a_ P est la topologie la moins fine, d'ofl q~r, M/N Soit est local, et si ~ ~ q A . Puisque , d'oG aussi est distinct de m B ~ ~ A =0 Cela r@sulte du corollaire pr@c@dent.

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Algèbre locale, multiplicités by Jean-Pierre Serre, Pierre Gabriel

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