Local homology and cohomology on schemes
Alonso Tarrío, Leovigildo ; Jeremías López, Ana ; Lipman, Joseph
Annales scientifiques de l'École Normale Supérieure, Tome 30 (1997), p. 1-39 / Harvested from Numdam
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@article{ASENS_1997_4_30_1_1_0,
     author = {Alonso Tarr\'\i o, Leovigildo and Jerem\'\i as L\'opez, Ana and Lipman, Joseph},
     title = {Local homology and cohomology on schemes},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {30},
     year = {1997},
     pages = {1-39},
     doi = {10.1016/s0012-9593(97)89914-4},
     mrnumber = {98d:14028},
     zbl = {0894.14002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1997_4_30_1_1_0}
}

Alonso Tarrío, Leovigildo; Jeremías López, Ana; Lipman, Joseph. Local homology and cohomology on schemes. Annales scientifiques de l'École Normale Supérieure, Tome 30 (1997) pp. 1-39. doi : 10.1016/s0012-9593(97)89914-4. http://gdmltest.u-ga.fr/item/ASENS_1997_4_30_1_1_0/

[BN] M. Bökstedt and A. Neeman, Homotopy limits in triangulated categories (Compositio Math., Vol. 86, 1993, pp. 209-234). | Numdam | MR 94f:18008 | Zbl 0802.18008

[Gl] J. P. C. Greenlees, Tate cohomology in commutative algebra (J. Pure and Applied Algebra, Vol. 94, 1994, pp. 59-83). | MR 95j:13012 | Zbl 0822.13009

[GM] J. P. C. Greenlees and J. P. May, Derived functors of I-adic completion and local homology (J. Algebra, Vol. 149, 1992, pp. 438-453). | MR 93h:13009 | Zbl 0774.18007

[Go] R. Godement, Théorie des faisceaux (Act. Sci. et Industrielles, no. 1252, Hermann Paris, 1964).

[Gr] A. Grothendieck, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2) (North-Holland Amsterdam, 1962). | MR 57 #16294 | Zbl 0197.47202

[EGA] A. Grothendieck and J. Dieudonné, Éléments de Géométrie Algébrique III (Publications Math. IHES, 11, 1961). | Numdam

[GrD] A. Grothendieck and J. Dieudonné, Éléments de Géométrie Algébrique I (Springer Verlag, New York, 1971). | Zbl 0203.23301

[H] R. Hartshorne, Residues and Duality (Lecture Notes in Math., no. 20, Springer-Verlag, New York, 1966). | MR 36 #5145 | Zbl 0212.26101

[H2] R. Hartshorne, Affine duality and cofiniteness (Inventiones Math., Vol. 9, 1970, pp. 145-164). | MR 41 #1750 | Zbl 0196.24301

[H3] R. Hartshorne, On the de Rham cohomology of algebraic varieties (Publications Math. IHES, Vol. 45, 1976, pp. 5-99). | Numdam | MR 55 #5633 | Zbl 0326.14004

[HK] R. Hübl and E. Kunz, Integration of differential forms on schemes (J. reine angew. Math., Vol. 410, 1990, pp. 53-83). | MR 92a:14014 | Zbl 0712.14006

[HS] R. Hübl and P. Sastry, Regular differential forms and relative duality (American J. Math., Vol. 115, 1993, pp. 749-787). | MR 94i:14022 | Zbl 0796.14012

[I] L. Illusie, Existence de Résolutions Globales, Théorie des Intersections et Théorème de Riemann-Roch (SGA 6) (Lecture Notes in Math., no. 225 Springer-Verlag, New York, 1971, pp. 160-221). | MR 50 #7133 | Zbl 0241.14002

[Ke] G. R. Kempf, Some elementary proofs of basic theorems in the cohomology of quasi-coherent sheaves, Rocky Mountain (J. Math, Vol. 10, 1980, pp. 637-645). | MR 81m:14015 | Zbl 0465.14008

[Ki] R. Kiehl, Ein “Descente”-Lemma und Grothendiecks Projektionssatz für nichtnoethersche Schemata (Math. Annalen, Vol. 198, 1972, pp. 287-316). | MR 52 #3165 | Zbl 0246.14002

[L] J. Lipman, Notes on Derived Categories and Derived Functors, preprint.

[L2] J. Lipman, Desingularization of two-dimensional schemes (Annals of Math., Vol. 107, 1978, pp. 151-207). | MR 58 #10924 | Zbl 0349.14004

[L3] J. Lipman, Dualizing Sheaves, Differentials, and Residues on Algebraic Varieties (Astérisque, vol. 117, Soc. Math. de France, 1984). | MR 86g:14008 | Zbl 0562.14003

[Lü] W. Lütkebohmert, On compactification of schemes (Manuscripta Math., Vol. 80, 1993, pp. 95-111). | MR 94h:14004 | Zbl 0822.14010

[M] E. Matlis, The Koszul complex and duality (Communications in Algebra, Vol. 1, 1974, pp. 87-144). | MR 49 #8980 | Zbl 0277.13011

[M2] E. Matlis, The higher properties of R-sequences (J. Algebra, Vol. 50, 1978, pp. 77-112). | MR 80a:13013 | Zbl 0384.13002

[Me] Z. Mebkhout Le théorème de positivité de l'irregularité pour les Dx-modules (The Grothendieck Festschrift, Volume III, Birkhäuser Boston, 1990, pp. 83-132). | MR 92j:32031 | Zbl 0731.14007

[N] A. Neeman, The Grothendieck duality theorem via Bousfield's techniques and Brown representability (Jour. Amer. Math. Soc., Vol. 9, 1996, pp. 205-236). | MR 96c:18006 | Zbl 0864.14008

[PS] C. Peskine and L. Szpiro, Dimension projective finie et cohomologie locale (Publications Math. IHES, Vol. 42, 1973, pp. 47-119). | Numdam | MR 51 #10330 | Zbl 0268.13008

[Sp] N. Spaltenstein, Resolutions of unbounded complexes (Compositio Mathematica, Vol. 65, 1988, pp. 121-154). | Numdam | MR 89m:18013 | Zbl 0636.18006

[St] R. Strebel, On homological duality (J. Pure and Applied Algebra, Vol. 8, 1976, pp. 75-96). | MR 54 #5319 | Zbl 0331.18021

[V] J.-L Verdier, Base change for twisted inverse image of coherent sheaves (Algebraic Geometry, Bombay Colloquium, 1968, Oxford University Press, London, 1969, pp. 393-408). | MR 43 #227 | Zbl 0202.19902