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Kleiman, Steven L.

Relative duality for quasi-coherent sheaves. (English) Zbl 0403.14003

Compos. Math. 41, 39-60 (1980).
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Cited in 4 Reviews
Cited in 41 Documents

MSC:

14F99 (Co)homology theory in algebraic geometry
14F20 Étale and other Grothendieck topologies and (co)homologies
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials

Keywords:

Quasi-Coherent Sheaf; Cohen-Macaulay; Duality Theory; Cohomology
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References:

[1] A. Altman and S. Kleiman : Introduction to Grothendieck Duality Theory . Lecture Notes in Math. 146, Springer (1970). · Zbl 0215.37201 · doi:10.1007/BFb0060932
[2] A. Altman and S. Kleiman : ” Compactifying the Picard scheme ”, (to appear in Adv. Math.). · Zbl 0427.14015 · doi:10.1016/0001-8708(80)90043-2
[3] P. Berthelot , et alii, Theorie des Intersections et Théorème de Riemann-Roch , Lecture Notes in Math. 225, Springer (1971). · Zbl 0218.14001
[4] P. Deligne and M. Rapoport : ” Les Schémas de Modules de Courbes Elliptiques ”, in Modular Functions of One Variable II , Lecture Notes in Math 349, Springer (1973). · Zbl 0281.14010
[5] M. Demazure and A. Grothendieck , Schémas en Groupes I , Lecture Notes in Math. 151, Springer (1970). · Zbl 0207.51401 · doi:10.1007/BFb0058993
[6] R. Godement , Topologie Algébrique et Théorie des Faisceaux , Hermann, Paris (1958). · Zbl 0080.16201
[7] A. Grothendieck , Théorème de dualité pour les faisceaux algébriques cohérents ”, Seminaire Bourbaki, 149 (May 1957). · Zbl 0227.14014
[8] A. Grothendieck , ” Technique de descente et théorèmes d’existence en géométrie algébrique IV. Les schémas de Hilbert ”, Séminaire Bourbaki 221 (May 1961). · Zbl 0236.14003
[9] A. Grothendieck and J. Dieudonné : Eléments de Géométrie Algébrique I , Grundlehren der math. Wissenschaften 166, Springer (1971). · Zbl 0203.23301
[10] A. Grothendieck and J. Dieudonné : Eléments de Géométrie Algébrique , Publ. Math. I.H.E.S., Nos. 8, 11, 17, 20, 24, 28, 32 (1961, ’61, ’63, ’64, ’65, ’66, ’67). | · Zbl 0203.23301
[11] R. Hartshorne : Residues and Duality , Lecture Notes in Math. 20, Springer (1966). · Zbl 0212.26101 · doi:10.1007/BFb0080482
[12] K. Lønsted and S. Kleiman : ” Basics on Families of Hyperelliptic Curves ”, Compositio Math., 38(1) (1979) 83-111. · Zbl 0406.14017
[13] S. Maclane : Categories for the Working Mathematician , Graduate Texts in Math. 5, Springer (1971). · Zbl 0232.18001
[14] A. Mattuck : ” Secant Bundles on Symmetric Products ”, American Journal Math., LXXXVII, 4 (1965), 779-797. · Zbl 0196.53503 · doi:10.2307/2373245
[15] D. Mumford : Lectures on Curves on an Algebraic Surface , Annals of Math. Studies No. 59, Princeton Univ. Press (1966). · Zbl 0187.42701 · doi:10.1515/9781400882069
[16] J.-L. Verdier : ” Duality dans la cohomologie des espaces localement compacts ”, Séminaire Bourbaki, 300 (Nov. 1965). · Zbl 0268.55006
[17] J.-L. Verdier : ” Base change for twisted inverse image of coherent sheaves ”, in Algebraic Geometry , Bombay 1968, Oxford (1969), 393-408. · Zbl 0202.19902
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