Skip to main content
Log in

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Bibliography

  1. M. F. Atiyah, Complex analytic connections in fibre bundles,Trans. Amer. Math. Soc.,85 (1957), 181–207.

    Article  MATH  Google Scholar 

  2. M. F. Atiyah andW. V. D. Hodge, Integrals of the second kind on an algebraic variety,Ann. of Math.,62 (1955), 56–91.

    Article  Google Scholar 

  3. W. Barth, Transplanting cohomology classes in complex projective space,Amer. J. Math.,92 (1970), 951–967.

    Article  MATH  Google Scholar 

  4. P. Berthelot, Cohomologiep-cristalline des schémas,C. R. Acad. Sci. Paris,269 (1969), 297–300; 357–360; 397–400.

    MATH  Google Scholar 

  5. T. Bloom andM. Herrera, De Rham cohomology of an analytic space,Inv. Math.,7 (1969), 275–296.

    Article  Google Scholar 

  6. A. Borel andJ. Moore, Homology theory for locally compact spaces,Mich. Math. J.,7 (1960), 137–159.

    Article  MATH  Google Scholar 

  7. A. Borel andJ.-P. Serre, Le théorème de Riemann-Roch,Bull. Soc. Math. France,86 (1958), 97–136.

    MATH  Google Scholar 

  8. E. Brieskorn, Die Monodromie der isolierten Singularitäten von Hyperflächen,Manuscripta Math.,2 (1970), 103–161.

    Article  MATH  Google Scholar 

  9. C. Chevalley,Anneaux de Chow et applications, Séminaire Chevalley, 1958.

  10. P. Deligne, Equations différentielles à points singuliers réguliers,Springer Lecture Notes,163 (1970), 133 p.

  11. J. Frisch, Points de platitude d’un morphisme d’espaces analytiques complexes,Inv. Math.,4 (1967), 118–138.

    Article  MATH  Google Scholar 

  12. R. Godement,Topologie algébrique et théorie des faisceaux, Hermann, Paris, 1958.

    MATH  Google Scholar 

  13. H. Grauert, Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen,Publ. Math. I.H.E.S.,5 (1960), 5–64.

    Google Scholar 

  14. A. Grothendieck, Sur quelques points d’algèbre homologique,Tohoku Math. J.,9 (1957), 119–221.

    MATH  Google Scholar 

  15. ———, La théorie des classes de Chern,Bull. Soc. Math. France,86 (1958), 137–154.

    MATH  Google Scholar 

  16. ———, On the De Rham cohomology of algebraic varieties,Publ. Math. I.H.E.S.,29 (1966), 95–103.

    Google Scholar 

  17. ---, Local Cohomology (LC),Springer Lecture Notes,41 (1966).

  18. ---, Crystals and the De Rham cohomology of schemes (Notes byI. Coates andO. Jussila) inDix exposés sur la cohomologie des schémas, North-Holland, 1968.

  19. ---, Revêtements étales et groupe fondamental (SGA 1),Springer Lecture Notes,224 (1971), 447 p.

  20. --- andJ. Dieudonné, Eléments de géométrie algébrique (EGA),Publ. Math. I.H.E.S.,4, 8, 11, 17, 20, 24, 28, 32 (1960–1967).

  21. R. C. Gunning andH. Rossi,Analytic functions of several complex variables, Prentice-Hall, 1965.

  22. R. Hartshorne, Residues and Duality (RD),Springer Lecture Notes,20 (1966).

  23. ———, Cohomological dimension of algebraic varieties,Annals of Math.,88 (1968), 403–450.

    Article  Google Scholar 

  24. ---, Ample subvarieties of algebraic varieties,Springer Lecture Notes,156 (1970).

  25. ———, Cohomology of non-complete algebraic varieties,Compositio Math.,23 (1971), 257–264.

    MATH  Google Scholar 

  26. ———, Cohomology with compact supports for coherent sheaves on an algebraic variety,Math. Ann.,195 (1972), 199–207.

    Article  MATH  Google Scholar 

  27. ———, Algebraic De Rham cohomology,Manuscripta Math.,7 (1972), 125–140.

    Article  MATH  Google Scholar 

  28. ———, Topological conditions for smoothing algebraic singularities,Topology,13 (1974), 241–253.

    Article  MATH  Google Scholar 

  29. M. Herrera andD. Lieberman, Duality and the De Rham cohomology of infinitesimal neighborhoods,Invent. Math.,13 (1971), 97–124.

    Article  MATH  Google Scholar 

  30. H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, I, II,Annals of Math.,79 (1964), 109–326.

    Article  Google Scholar 

  31. G. Hochschild, B. Kostant andA. Rosenberg, Differential forms on regular affine algebras,Trans. Amer. Math. Soc.,102 (1962), 383–408.

    Article  MATH  Google Scholar 

  32. N. Katz, Nilpotent connections and the monodromy theorem: applications of a result of Turrittin,Publ. Math. I.H.E.S.,39 (1970), 175–232.

    MATH  Google Scholar 

  33. ———, The regularity theorem in algebraic geometry,Proc. Int. Cong. Math. in Nice, 1970, vol. 1, 437–443.

    Google Scholar 

  34. ——— andT. Oda, On the differentiation of De Rham cohomology classes with respect to parameters,J. Math. Kyoto Univ.,8 (1968), 199–213.

    MATH  Google Scholar 

  35. L. Kamp, Eine topologische Eigenschaft Steinscher Räume,Nachr. Akad. Wiss. Göttingen,8 (1966).

  36. R. Kiehl, Note zu der Arbeit von J. Frisch « Points de platitude d’un morphisme d’espaces analytiques complexes »,Inv. Math.,4 (1967), 139–141.

    Article  MATH  Google Scholar 

  37. I. G. Macdonald, Duality over complete local rings,Topology,1 (1962), 213–235.

    Article  MATH  Google Scholar 

  38. P. Monsky, Formal cohomology II,Annals of Math.,88 (1968), 218–238.

    Article  Google Scholar 

  39. ———, Finiteness of De Rham cohomology,Amer. J. Math.,94 (1972), 237–245.

    Article  MATH  Google Scholar 

  40. M. Nagata, Imbedding of an abstract variety in a complete variety,J. Math. Kyoto Univ.,2 (1962), 1–10.

    MATH  Google Scholar 

  41. ———, A generalization of the embedding problem,J. Math. Kyoto Univ.,3 (1963), 89–102.

    MATH  Google Scholar 

  42. R. Narasimhan, On the homology groups of Stein spaces,Inv. Math.,2 (1967), 377–385.

    Article  MATH  Google Scholar 

  43. A. Ogus,Local cohomological dimension of algebraic varieties, Thesis, Harvard, 1972. Added in proof: These results are published in two papers:

  44. A. Ogus, Local cohomological dimension of algebraic varieties,Annals of Math.,98 (1973), 327–365.

    Article  Google Scholar 

  45. ---, On the formal neighborhood of a subvariety of projective space (to appear inAmer. J. Math.).

  46. H.-J. Reiffen, Das Lemma von Poincaré für holomorphe Differentialformen auf Komplexen Räumen,Math. Zeit.,101 (1967), 269–284.

    Article  MATH  Google Scholar 

  47. J.-E. Roos, Sur les foncteurs dérivés de lim. Applications.C. R. Acad. Sc. Paris,252 (1961), 3702–3704.

    MATH  Google Scholar 

  48. J.-P. Serre, Faisceaux algébriques cohérents (FAC),Annals of Math.,61 (1955), 197–278.

    Article  Google Scholar 

  49. ———, Géométrie algébrique et géométrie analytique (GAGA),Ann. Inst. Fourier,6 (1956), 1–42.

    Google Scholar 

  50. E. H. Spanier,Algebraic Topology, McGraw-Hill, 1966.

  51. D. Lieberman, Generalizations of the De Rham complex with applications to duality theory and the cohomology of singular varieties,Proc. Conf. of Complex Analysis, Rice, 1972.

Download references

Authors

About this article

Cite this article

Hartshorne, R. On the de rham cohomology of algebraic varieties. Publications Mathématiques de L’Institut des Hautes Scientifiques 45, 6–99 (1975). https://doi.org/10.1007/BF02684298

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02684298

Keywords

Navigation