Local homology and cohomology on schemes
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 30 (1997) no. 1, pp. 1-39.
@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},
     pages = {1--39},
     publisher = {Elsevier},
     volume = {Ser. 4, 30},
     number = {1},
     year = {1997},
     doi = {10.1016/s0012-9593(97)89914-4},
     mrnumber = {98d:14028},
     zbl = {0894.14002},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(97)89914-4/}
}
TY  - JOUR
AU  - Alonso Tarrío, Leovigildo
AU  - Jeremías López, Ana
AU  - Lipman, Joseph
TI  - Local homology and cohomology on schemes
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1997
SP  - 1
EP  - 39
VL  - 30
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/s0012-9593(97)89914-4/
DO  - 10.1016/s0012-9593(97)89914-4
LA  - en
ID  - ASENS_1997_4_30_1_1_0
ER  - 
%0 Journal Article
%A Alonso Tarrío, Leovigildo
%A Jeremías López, Ana
%A Lipman, Joseph
%T Local homology and cohomology on schemes
%J Annales scientifiques de l'École Normale Supérieure
%D 1997
%P 1-39
%V 30
%N 1
%I Elsevier
%U http://www.numdam.org/articles/10.1016/s0012-9593(97)89914-4/
%R 10.1016/s0012-9593(97)89914-4
%G en
%F 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, Série 4, Tome 30 (1997) no. 1, pp. 1-39. doi : 10.1016/s0012-9593(97)89914-4. http://www.numdam.org/articles/10.1016/s0012-9593(97)89914-4/

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

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

[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 | Zbl

[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 | Zbl

[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

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

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

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

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

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

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

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

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

[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 | Zbl

[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 | Zbl

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

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

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

[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 | Zbl

Cité par Sources :