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A modification of Grothendieck’s spectral sequence

Published online by Cambridge University Press:  22 January 2016

Edgar Enochs
Edgar Enochs*
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-6027, U.S.A.
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Let C, C′ and C″ be abelian categories where C and C′ have enough injectives and let F: C → C′, G: C′ → C″ be additive covariant functors. Then for an object X of C, let C(X) be the complex associated with an injective resolution of X. Grothendieck gets a first quadrant spectral sequence by taking an injective resolution of the complex F(C(X)) and applying G to the associated double complex.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 112 , December 1988 , pp. 53 - 61
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

[1] Grothendieck, A., Sur quelques points d’algèbre homologique, Tôhoku Math. J., Series 2, 9, No. 2 (1957), 119–221.Google Scholar
[2] Grothendieck, A., Local Cohomology (notes by Hartshorne, R.).Google Scholar
[3] Roberts, P., Homological invariants of modules over commutative rings, Séminaire de mathématiques supérieures, L’Université de Montréal (1980).Google Scholar
[4] Eisenbud, D., Complete intersections, Trans. Amer. Math. Soc., 260 (1980), 35–64.CrossRefGoogle Scholar
[5] Ramras, M., Sequences of Betti numbers, J. Algebra, 66 (1980), 193–204.CrossRefGoogle Scholar
[6] Enochs, E., Injective and flat covers, envelopes and resolvents, Israel J. Math., 39 (8)(1981), 189–209.CrossRefGoogle Scholar
[7] Dold, A., Universelle Koeffizienten, Math. Z., 80 (1962), 63–88.Google Scholar
[8] Brualdi, R., Introductory Combinatorics, North Holland, New York, 1977.Google Scholar
[9] Foxby, H., On the μi in a minimal injective resolution, Math. Scand., 29 (1971), 175–186.CrossRefGoogle Scholar
[10] Cartan, H. and Eilenberg, S., Homological Algebra, Princeton Math. Ser. 19, Princeton, 1956.Google Scholar
[11] Alperin, J. L. and Janusz, G. J., Resolutions and periodicity, Proc. Amer. Math. Soc., 37 (1973), 403–406.CrossRefGoogle Scholar
[12] Curtis, C. W. and Reiner, I., Methods of Representation Theory, Vol. I, John Wiley and Sons, New York, 1981.Google Scholar