×
Hartshorne, Robin

On the De Rham cohomology of algebraic varieties. (English) Zbl 0326.14004

Publ. Math., Inst. Hautes Étud. Sci. 45, 5-99 (1975).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0326.14004

Cited in 5 Reviews
Cited in 98 Documents

MSC:

14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
14F25 Classical real and complex (co)homology in algebraic geometry
14B20 Formal neighborhoods in algebraic geometry
14B05 Singularities in algebraic geometry
PDF BibTeX XML Cite
\textit{R. Hartshorne}, Publ. Math., Inst. Hautes Étud. Sci. 45, 5--99 (1975; Zbl 0326.14004)
Full Text: DOI Numdam EuDML

References:

[1] M. F. Atiyah, Complex analytic connections in fibre bundles,Trans. Amer. Math. Soc.,85 (1957), 181–207. · Zbl 0078.16002
[2] M. F. Atiyah andW. V. D. Hodge, Integrals of the second kind on an algebraic variety,Ann. of Math.,62 (1955), 56–91. · Zbl 0068.34401
[3] W. Barth, Transplanting cohomology classes in complex projective space,Amer. J. Math.,92 (1970), 951–967. · Zbl 0206.50001
[4] P. Berthelot, Cohomologiep-cristalline des schémas,C. R. Acad. Sci. Paris,269 (1969), 297–300; 357–360; 397–400. · Zbl 0179.26202
[5] T. Bloom andM. Herrera, De Rham cohomology of an analytic space,Inv. Math.,7 (1969), 275–296. · Zbl 0175.37301
[6] A. Borel andJ. Moore, Homology theory for locally compact spaces,Mich. Math. J.,7 (1960), 137–159. · Zbl 0116.40301
[7] A. Borel andJ.-P. Serre, Le théorème de Riemann-Roch,Bull. Soc. Math. France,86 (1958), 97–136. · Zbl 0091.33004
[8] E. Brieskorn, Die Monodromie der isolierten Singularitäten von Hyperflächen,Manuscripta Math.,2 (1970), 103–161. · Zbl 0186.26101
[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. · Zbl 0244.14004
[11] J. Frisch, Points de platitude d’un morphisme d’espaces analytiques complexes,Inv. Math.,4 (1967), 118–138. · Zbl 0167.06803
[12] R. Godement,Topologie algébrique et théorie des faisceaux, Hermann, Paris, 1958. · Zbl 0080.16201
[13] H. Grauert, Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen,Publ. Math. I.H.E.S.,5 (1960), 5–64. · Zbl 0158.32901
[14] A. Grothendieck, Sur quelques points d’algèbre homologique,Tohoku Math. J.,9 (1957), 119–221. · Zbl 0118.26104
[15] ——, La théorie des classes de Chern,Bull. Soc. Math. France,86 (1958), 137–154. · Zbl 0091.33201
[16] ——, On the De Rham cohomology of algebraic varieties,Publ. Math. I.H.E.S.,29 (1966), 95–103. · Zbl 0145.17602
[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. · Zbl 0141.08601
[22] R. Hartshorne, Residues and Duality (RD),Springer Lecture Notes,20 (1966). · Zbl 0212.26101
[23] ——, Cohomological dimension of algebraic varieties,Annals of Math.,88 (1968), 403–450. · Zbl 0169.23302
[24] —, Ample subvarieties of algebraic varieties,Springer Lecture Notes,156 (1970). · Zbl 0208.48901
[25] ——, Cohomology of non-complete algebraic varieties,Compositio Math.,23 (1971), 257–264. · Zbl 0221.14014
[26] ——, Cohomology with compact supports for coherent sheaves on an algebraic variety,Math. Ann.,195 (1972), 199–207. · Zbl 0254.14010
[27] ——, Algebraic De Rham cohomology,Manuscripta Math.,7 (1972), 125–140. · Zbl 0237.14008
[28] ——, Topological conditions for smoothing algebraic singularities,Topology,13 (1974), 241–253. · Zbl 0288.14006
[29] M. Herrera andD. Lieberman, Duality and the De Rham cohomology of infinitesimal neighborhoods,Invent. Math.,13 (1971), 97–124. · Zbl 0218.32005
[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. · Zbl 0122.38603
[31] G. Hochschild, B. Kostant andA. Rosenberg, Differential forms on regular affine algebras,Trans. Amer. Math. Soc.,102 (1962), 383–408. · Zbl 0102.27701
[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. · Zbl 0221.14007
[33] ——, The regularity theorem in algebraic geometry,Proc. Int. Cong. Math. in Nice, 1970, vol. 1, 437–443.
[34] —— andT. Oda, On the differentiation of De Rham cohomology classes with respect to parameters,J. Math. Kyoto Univ.,8 (1968), 199–213. · Zbl 0165.54802
[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.} · Zbl 0167.06901
[37] I. G. Macdonald, Duality over complete local rings,Topology,1 (1962), 213–235. · Zbl 0108.26401
[38] P. Monsky, Formal cohomology II,Annals of Math.,88 (1968), 218–238. · Zbl 0162.52601
[39] ——, Finiteness of De Rham cohomology,Amer. J. Math.,94 (1972), 237–245. · Zbl 0241.14010
[40] M. Nagata, Imbedding of an abstract variety in a complete variety,J. Math. Kyoto Univ.,2 (1962), 1–10. · Zbl 0109.39503
[41] ——, A generalization of the embedding problem,J. Math. Kyoto Univ.,3 (1963), 89–102. · Zbl 0223.14011
[42] R. Narasimhan, On the homology groups of Stein spaces,Inv. Math.,2 (1967), 377–385. · Zbl 0148.32202
[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. · Zbl 0308.14003
[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. · Zbl 0164.09401
[47] J.-E. Roos, Sur les foncteurs dérivés de lim. Applications.C. R. Acad. Sc. Paris,252 (1961), 3702–3704. · Zbl 0102.02501
[48] J.-P. Serre, Faisceaux algébriques cohérents (FAC),Annals of Math.,61 (1955), 197–278. · Zbl 0067.16201
[49] ——, Géométrie algébrique et géométrie analytique (GAGA),Ann. Inst. Fourier,6 (1956), 1–42.
[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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.