Local homology and cohomology on schemes

Leovigildo Alonso Tarrío; Ana Jeremías López; Joseph Lipman

Annales scientifiques de l'École Normale Supérieure (1997)

  • Volume: 30, Issue: 1, page 1-39
  • ISSN: 0012-9593

How to cite

top

Alonso Tarrío, Leovigildo, Jeremías López, Ana, and Lipman, Joseph. "Local homology and cohomology on schemes." Annales scientifiques de l'École Normale Supérieure 30.1 (1997): 1-39. <http://eudml.org/doc/82425>.

@article{AlonsoTarrío1997,
author = {Alonso Tarrío, Leovigildo, Jeremías López, Ana, Lipman, Joseph},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {quasi-compact scheme; formal scheme; Koszul complex; proregular sequence; local cohomology; local homology; adjointness; derived functor; Bousfield localization; Matlis duality; Grothendieck duality; Warwick duality theorem; Peskine-Szpiro duality; functorial duality},
language = {eng},
number = {1},
pages = {1-39},
publisher = {Elsevier},
title = {Local homology and cohomology on schemes},
url = {http://eudml.org/doc/82425},
volume = {30},
year = {1997},
}

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
PB - Elsevier
VL - 30
IS - 1
SP - 1
EP - 39
LA - eng
KW - quasi-compact scheme; formal scheme; Koszul complex; proregular sequence; local cohomology; local homology; adjointness; derived functor; Bousfield localization; Matlis duality; Grothendieck duality; Warwick duality theorem; Peskine-Szpiro duality; functorial duality
UR - http://eudml.org/doc/82425
ER -

References

top
  1. [BN] M. BÖKSTEDT and A. NEEMAN, Homotopy limits in triangulated categories (Compositio Math., Vol. 86, 1993, pp. 209-234). Zbl0802.18008MR94f:18008
  2. [Gl] J. P. C. GREENLEES, Tate cohomology in commutative algebra (J. Pure and Applied Algebra, Vol. 94, 1994, pp. 59-83). Zbl0822.13009MR95j:13012
  3. [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). Zbl0774.18007MR93h:13009
  4. [Go] R. GODEMENT, Théorie des faisceaux (Act. Sci. et Industrielles, no. 1252, Hermann Paris, 1964). 
  5. [Gr] A. GROTHENDIECK, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2) (North-Holland Amsterdam, 1962). Zbl0197.47202MR57 #16294
  6. [EGA] A. GROTHENDIECK and J. DIEUDONNÉ, Éléments de Géométrie Algébrique III (Publications Math. IHES, 11, 1961). 
  7. [GrD] A. GROTHENDIECK and J. DIEUDONNÉ, Éléments de Géométrie Algébrique I (Springer Verlag, New York, 1971). Zbl0203.23301
  8. [H] R. HARTSHORNE, Residues and Duality (Lecture Notes in Math., no. 20, Springer-Verlag, New York, 1966). Zbl0212.26101MR36 #5145
  9. [H2] R. HARTSHORNE, Affine duality and cofiniteness (Inventiones Math., Vol. 9, 1970, pp. 145-164). Zbl0196.24301MR41 #1750
  10. [H3] R. HARTSHORNE, On the de Rham cohomology of algebraic varieties (Publications Math. IHES, Vol. 45, 1976, pp. 5-99). Zbl0326.14004MR55 #5633
  11. [HK] R. HÜBL and E. KUNZ, Integration of differential forms on schemes (J. reine angew. Math., Vol. 410, 1990, pp. 53-83). Zbl0712.14006MR92a:14014
  12. [HS] R. HÜBL and P. SASTRY, Regular differential forms and relative duality (American J. Math., Vol. 115, 1993, pp. 749-787). Zbl0796.14012MR94i:14022
  13. [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). Zbl0241.14002MR50 #7133
  14. [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). Zbl0465.14008MR81m:14015
  15. [Ki] R. KIEHL, Ein “Descente”-Lemma und Grothendiecks Projektionssatz für nichtnoethersche Schemata (Math. Annalen, Vol. 198, 1972, pp. 287-316). Zbl0246.14002MR52 #3165
  16. [L] J. LIPMAN, Notes on Derived Categories and Derived Functors, preprint. 
  17. [L2] J. LIPMAN, Desingularization of two-dimensional schemes (Annals of Math., Vol. 107, 1978, pp. 151-207). Zbl0349.14004MR58 #10924
  18. [L3] J. LIPMAN, Dualizing Sheaves, Differentials, and Residues on Algebraic Varieties (Astérisque, vol. 117, Soc. Math. de France, 1984). Zbl0562.14003MR86g:14008
  19. [Lü] W. LÜTKEBOHMERT, On compactification of schemes (Manuscripta Math., Vol. 80, 1993, pp. 95-111). Zbl0822.14010MR94h:14004
  20. [M] E. MATLIS, The Koszul complex and duality (Communications in Algebra, Vol. 1, 1974, pp. 87-144). Zbl0277.13011MR49 #8980
  21. [M2] E. MATLIS, The higher properties of R-sequences (J. Algebra, Vol. 50, 1978, pp. 77-112). Zbl0384.13002MR80a:13013
  22. [Me] Z. MEBKHOUTLe théorème de positivité de l'irregularité pour les Dx-modules (The Grothendieck Festschrift, Volume III, Birkhäuser Boston, 1990, pp. 83-132). Zbl0731.14007MR92j:32031
  23. [N] A. NEEMAN, The Grothendieck duality theorem via Bousfield's techniques and Brown representability (Jour. Amer. Math. Soc., Vol. 9, 1996, pp. 205-236). Zbl0864.14008MR96c:18006
  24. [PS] C. PESKINE and L. SZPIRO, Dimension projective finie et cohomologie locale (Publications Math. IHES, Vol. 42, 1973, pp. 47-119). Zbl0268.13008MR51 #10330
  25. [Sp] N. SPALTENSTEIN, Resolutions of unbounded complexes (Compositio Mathematica, Vol. 65, 1988, pp. 121-154). Zbl0636.18006MR89m:18013
  26. [St] R. STREBEL, On homological duality (J. Pure and Applied Algebra, Vol. 8, 1976, pp. 75-96). Zbl0331.18021MR54 #5319
  27. [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). Zbl0202.19902MR43 #227

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.