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portada Homologie des Algebres Commutatives (in French)
Type
Physical Book
Publisher
Author
Year
2017
Language
French
Pages
15
Format
Paperback
ISBN13
9783642514500
Edition No.
1èr
Categories

Homologie des Algebres Commutatives (in French)

M. Andre (Author) · Springer · Paperback

Homologie des Algebres Commutatives (in French) - M. Andre

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Synopsis "Homologie des Algebres Commutatives (in French)"

(egalite 3. 4). Ce complexe T*(A, B) per met de definir les modules d'homo- logie de l'algebre (definition 3. 11) Hn(A, B, W) = Yt, [T*(A, B)@B W] et les modules de cohomologie de l'algebre (definition 3. 12) Hn(A, B, W) = Yfn[HomB(T*(A, B), W)]. En particulier l'homologie et la cohomologie d'une algebre libre sont triviales (corollaire 3. 36). Quant au module Ho(A, B, B) il est toujours isomorphe au module des differentielles de Kaehler QBIA (proposition 6. 3). Lorsque l'anneau Best un quotient de l'anneau A, la situation est simple en degre 1 (proposition 6. 1) H (A, B, W) Tor}(B, W) I et en degre 2 (theoreme 15. 8, propositions 15. 9 et 15. 12) H (A, B, W) Tor1(B, W)jTor}(B, B). Tor}(B, W). 2 En ajoutant des variables independantes a l'anneau A, il est d'ailleurs possible de se ramener a ce cas particulier (corollaire 5. 2). Dans cette theorie, les modules d'homologie relative sont en fait des modules d'homologie absolue. De maniere precise: a une A-algebre B et a une B-algebre C correspond une suite exacte, dite de Jacobi- Zariski (theoreme 5. 1) . . . --+ Hn(A, B, W) --+ Hn(A, C, W) --+ Hn(B, C, W) -+ H _ I (A, B, W) --+ ---- n De cette suite decoulent des relations entre differentielles de Kaehler (n = 0), algebres lisses (n = 1), anneaux reguliers (n = 2) et intersections completes (n = 3). Une autre propriete fondamentale est la suivante (proposition 4.

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