Algebra Lineal OEA 5 by Orlando E. Villamayor

By Orlando E. Villamayor

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6. 3. man nicht (0) Zur alle lokalen Komplex i e ~ . h. H nm(M) ~ 0 . notwendig, vorauszusetzen. 4 w e r d e n zutrifft. Integrit~tsbereiche gilt allgemeinen fHr R i n g e besitzen. (a) n i c h t des Andererseits Abschnitts Komplex M ~ 0 die E x i s t e n z Hbergeht. h. 6 Komplexes indem F~r Kohomolo~ie wir Komplexen die k o h o m o l o g i s c h e n A-Modul von von M A-Moduln definiert. h. Annullatoren Analog ai(M) erkl~ren al(M'). 1. Satz seitig Sei begrenzter M" Komplex : 0 ~ ... ,s ao(Mn) a l ( M n-l) A n n H O(M') Beweis.

Lemme [491 d a r s t e l l t , wir so- zus~tzlichen kohomologischen haben gibt, s D+(A) c Komplexen Aussagen ben@tigen. M" der Ringe dualisierenden aus Komplettie- hierzu sind yon endlich diese endlich Bereicherung Komplex des sich Kohomologie- noethersche zum Tell Kohomologie dass vergleiche fur e i n e n gestatten was eine fur R i n g e m i t unterscheidet I" lokale der Existenz ist 2 . 3 . 1 , I" notwendig besitzen, Eigenschaften hinaus Dualit[t dadurch, fur d e n F a l l zur l o k a l e n hiervon ist.

H o c h s t e r s Wir Komplex eine Anwendung yon M. liebenswerten LiebenswUrdigkeit, dualisierendem bildet den ist die Cohen-Macaulay-Moduln. rung der Kapitels dam Quotien- lokalen Ringes den K o s z u l - K o m - = {x~ ..... n und 0 < m < n = = bezUglich . der m u l t i p l i - 30 kativ abgeschlossenen wir K~ & A die injektive Menge . Schliesslich nat~rlicher HOlle Weise Isomorphismus {xrlr ~ 0} definieren wir des R e s t k l a s s e n k ~ r p e r s ^ A-Modul-Struktur, Insbesondere bemerken I" = H O m A ( K ' , E ) , wobei E bezeichnet.

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