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A modification of Grothendieck’s spectral sequence. (English) Zbl 0628.18009

Using a mix of projective and injective resolutions, Grothendieck’s spectral sequence can be modified to give several results. These include a generalized version of Grothendieck duality, an inequality concerning the growth of Betti numbers and information about syzygies of finitely generated modules over Gorenstein rings.

MSC:

18G40 Spectral sequences, hypercohomology
18E10 Abelian categories, Grothendieck categories
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
18G05 Projectives and injectives (category-theoretic aspects)
18G10 Resolutions; derived functors (category-theoretic aspects)
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References:

[1] Math. Scand. 29 pp 175– (1971) · Zbl 0235.13006 · doi:10.7146/math.scand.a-11043
[2] Introductory Combinatorics (1977) · Zbl 0385.05001
[3] Universelle Koeffizienten, Math. Z. 80 pp 63– (1962)
[4] DOI: 10.1007/BF02760849 · Zbl 0464.16019 · doi:10.1007/BF02760849
[5] DOI: 10.1016/0021-8693(80)90119-2 · Zbl 0474.13007 · doi:10.1016/0021-8693(80)90119-2
[6] Princeton Math. Ser. 19 (1956)
[7] Séminaire de mathématiques supérieures (1980)
[8] Tôhoku Math. J. 9 pp 119– (1957)
[9] Methods of Representation Theory I (1981)
[10] DOI: 10.1090/S0002-9939-1973-0320178-1 · doi:10.1090/S0002-9939-1973-0320178-1
[11] DOI: 10.1090/S0002-9947-1980-0570778-7 · doi:10.1090/S0002-9947-1980-0570778-7
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