Geodesic
On dimension theory for complexes
Sbornik. Mathematics, Tome 36 (1980) no. 4, pp. 469-481 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Passage from the category of modules to the derived category gives insight into some classical results of homological dimension theory, and also yields a proof of the nondegeneracy of the Yoneda multiplication $\operatorname{Ext}_A^p(k,\,\cdot\,)\times\operatorname{Ext}_A^{n-p}(\,\cdot\,,k)\to\operatorname{Ext}_A^n(k,k)=k$, where the argument is a noetherian module (or a finite complex with noetherian homology) and $A$ is a regular local ring. Bibliography: 9 titles. 
@article{SM_1980_36_4_a1,
     author = {A. F. Ivanov},
     title = {On dimension theory for complexes},
     journal = {Sbornik. Mathematics},
     pages = {469--481},
     year = {1980},
     volume = {36},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1980_36_4_a1/}
}
TY  - JOUR
AU  - A. F. Ivanov
TI  - On dimension theory for complexes
JO  - Sbornik. Mathematics
PY  - 1980
SP  - 469
EP  - 481
VL  - 36
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1980_36_4_a1/
LA  - en
ID  - SM_1980_36_4_a1
ER  - 
%0 Journal Article
%A A. F. Ivanov
%T On dimension theory for complexes
%J Sbornik. Mathematics
%D 1980
%P 469-481
%V 36
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1980_36_4_a1/
%G en
%F SM_1980_36_4_a1
A. F. Ivanov. On dimension theory for complexes. Sbornik. Mathematics, Tome 36 (1980) no. 4, pp. 469-481. http://geodesic.mathdoc.fr/item/SM_1980_36_4_a1/

[1] J.-P. Serre, “Algébre locale”, Multiplicités, Lecture Notes in Math., 11, Springer-Verlag, Berlin–New York, 1965 | MR | Zbl

[2] M. Auslander, D. A. Buchsbaum, “Homological dimension in local rings. I”, Trans. Amer. Math. Soc., 85:2 (1957), 390–405 | DOI | MR | Zbl

[3] M. Auslander, D. A. Buchsbaum, “Codimension and Multiplicity”, Ann. Math., 68:3 (1958), 625–657 | DOI | MR | Zbl

[4] R. Hartshorne, “Residues and Duality”, Lecture Notes in Math., 20, Springer-Verlag, Berlin–New York, 1966 | MR | Zbl

[5] Chr. Peskine, L. Szpiro, Dimension projective finie et cohomologie locale, Thèse ..., Univ. Paris, 1971; Publ. Math., Inst. Hautes Étud. Sci., 42 (1972), 47–119 | Zbl

[6] S. Maklein, Gomologiya, izd-vo “Mir”, Moskva, 1966

[7] A. Kartan, S. Eilenberg, Gomologicheskaya algebra, IL, Moskva, 1960

[8] P. Gabriel, “Objets injectifs dans les categories abeliennes”, Sem. Dubreil–Pisot, exp. 17, 1958–1959

[9] M. Auslander, “Modules over unramified local rings”, Illinois J. Math., 5 (1961), 631–647 | MR | Zbl