On the de Rham cohomology of algebraic varieties
Hartshorne, Robin
Publications Mathématiques de l'IHÉS, Tome 45 (1975), p. 5-99 / Harvested from Numdam
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@article{PMIHES_1975__45__5_0,
     author = {Hartshorne, Robin},
     title = {On the de Rham cohomology of algebraic varieties},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {45},
     year = {1975},
     pages = {5-99},
     mrnumber = {55 \#5633},
     zbl = {0326.14004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_1975__45__5_0}
}

Hartshorne, Robin. On the de Rham cohomology of algebraic varieties. Publications Mathématiques de l'IHÉS, Tome 45 (1975) pp. 5-99. http://gdmltest.u-ga.fr/item/PMIHES_1975__45__5_0/

[1] M. F. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc., 85 (1957), 181-207. | MR 19,172c | Zbl 0078.16002

[2] M. F. Atiyah and W. V. D. Hodge, Integrals of the second kind on an algebraic variety, Ann. of Math., 62 (1955), 56-91. | MR 17,533d | Zbl 0068.34401

[3] W. Barth, Transplanting cohomology classes in complex projective space, Amer. J. Math., 92 (1970), 951-967. | MR 44 #4239 | Zbl 0206.50001

[4] P. Berthelot, Cohomologie p-cristalline des schémas, C. R. Acad. Sci. Paris, 269 (1969), 297-300 ; 357-360 ; 397-400. | MR 40 #151 | Zbl 0179.26301

[5] T. Bloom and M. Herrera, De Rham cohomology of an analytic space, Inv. Math., 7 (1969), 275-296. | MR 40 #1601 | Zbl 0175.37301

[6] A. Borel and J. Moore, Homology theory for locally compact spaces, Mich. Math. J., 7 (1960), 137-159. | MR 24 #A1123 | Zbl 0116.40301

[7] A. Borel and J.-P. Serre, Le théorème de Riemann-Roch, Bull. Soc. Math. France, 86 (1958), 97-136. | Numdam | MR 22 #6817 | Zbl 0091.33004

[8] E. Brieskorn, Die Monodromie der isolierten Singularitäten von Hyperflächen, Manuscripta Math., 2 (1970), 103-161. | MR 42 #2509 | 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. | MR 54 #5232 | Zbl 0244.14004

[11] J. Frisch, Points de platitude d'un morphisme d'espaces analytiques complexes, Inv. Math., 4 (1967), 118-138. | MR 36 #5388 | Zbl 0167.06803

[12] R. Godement, Topologie algébrique et théorie des faisceaux, Hermann, Paris, 1958. | MR 21 #1583 | 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. | Numdam | Zbl 0100.08001

[14] A. Grothendieck, Sur quelques points d'algèbre homologique, Tohoku Math. J., 9 (1957), 119-221. | MR 21 #1328 | Zbl 0118.26104

[15] A. Grothendieck, La théorie des classes de Chern, Bull. Soc. Math. France, 86 (1958), 137-154. | Numdam | MR 22 #6818 | Zbl 0091.33201

[16] A. Grothendieck, On the De Rham cohomology of algebraic varieties, Publ. Math. I.H.E.S., 29 (1966), 95-103. | Numdam | MR 33 #7343 | Zbl 0145.17602

[17] A. Grothendieck, Local Cohomology (LC), Springer Lecture Notes, 41 (1966). | MR 37 #219 | Zbl 0185.49202

[18] A. Grothendieck, Crystals and the De Rham cohomology of schemes (Notes by I. COATES and O. JUSSILA) in Dix exposés sur la cohomologie des schémas, North-Holland, 1968. | MR 42 #4558 | Zbl 0215.37102

[19] A. Grothendieck, Revêtements étales et groupe fondamental (SGA 1), Springer Lecture Notes, 224 (1971), 447 p. | MR 50 #7129 | Zbl 0234.14002

[20] A. Grothendieck and J. Dieudonné, Elements de géométrie algébrique (EGA), Publ. Math. I.H.E.S., 4, 8, 11, 17, 20, 24, 28, 32 (1960-1967). | Numdam

[21] R. C. Gunning and H. Rossi, Analytic functions of several complex variables, Prentice-Hall, 1965. | MR 31 #4927 | Zbl 0141.08601

[22] R. Hartshorne, Residues and Duality (RD), Springer Lecture Notes, 20 (1966). | MR 36 #5145 | Zbl 0212.26101

[23] R. Hartshorne, Cohomological dimension of algebraic varieties, Annals of Math., 88 (1968), 403-450. | MR 38 #1103 | Zbl 0169.23302

[24] R. Hartshorne, Ample subvarieties of algebraic varieties, Springer Lecture Notes, 156 (1970). | MR 44 #211 | Zbl 0208.48901

[25] R. Hartshorne, Cohomology of non-complete algebraic varieties, Compositio Math., 23 (1971), 257-264. | Numdam | MR 46 #1793 | Zbl 0221.14014

[26] R. Hartshorne, Cohomology with compact supports for coherent sheaves on an algebraic variety, Math. Ann., 195 (1972), 199-207. | MR 45 #6827 | Zbl 0254.14010

[27] R. Hartshorne, Algebraic De Rham cohomology, Manuscripta Math., 7 (1972), 125-140. | MR 47 #1810 | Zbl 0237.14008

[28] R. Hartshorne, Topological conditions for smoothing algebraic singularities, Topology, 13 (1974), 241-253. | MR 50 #2170 | Zbl 0288.14006

[29] M. Herrera and D. Lieberman, Duality and the De Rham cohomology of infinitesimal neighborhoods, Invent. Math., 13 (1971), 97-124. | MR 46 #9388 | 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. | MR 33 #7333 | Zbl 0122.38603

[31] G. Hochschild, B. Kostant and A. Rosenberg, Differential forms on regular affine algebras, Trans. Amer. Math. Soc., 102 (1962), 383-408. | MR 26 #167 | 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. | Numdam | MR 45 #271 | Zbl 0221.14007

[33] N. Katz, The regularity theorem in algebraic geometry, Proc. Int. Cong. Int. Cong. Math. in Nice, 1970, vol. 1, 437-443. | MR 57 #12512 | Zbl 0235.14006

[34] N. Katz and T. Oda, On the differentiation of De Rham cohomology classes with respect to parameters, J. Math. Kyoto Univ., 8 (1968), 199-213. | MR 38 #5792 | Zbl 0165.54802

[35] L. Kamp, Eine topologische Eigenschaft Steinscher Räume, Nachr. Akad. Wiss. Göttingen, 8 (1966). | Zbl 0146.31301

[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. | MR 36 #5389 | Zbl 0167.06901

[37] I. G. Macdonald, Duality over complete local rings, Topology, 1 (1962), 213-235. | MR 27 #1476 | Zbl 0108.26401

[38] P. Monsky, Formal cohomology II, Annals of Math., 88 (1968), 218-238. | Zbl 0162.52601

[39] P. Monsky, Finiteness of De Rham cohomology, Amer. J. Math., 94 (1972), 237-245. | MR 46 #177 | Zbl 0241.14010

[40] M. Nagata, Imbedding of an abstract variety in a complete variety, J. Math. Kyoto Univ., 2 (1962), 1-10. | MR 26 #118 | Zbl 0109.39503

[41] M. Nagata, A generalization of the embedding problem, J. Math. Kyoto Univ., 3 (1963), 89-102. | MR 28 #2114 | Zbl 0223.14011

[42] R. Narasimhan, On the homology groups of Stein spaces, Inv. Math., 2 (1967), 377-385. | MR 35 #7356 | 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 :

[43 a] A. Ogus, Local cohomological dimension of algebraic varieties, Annals of Math., 98 (1973), 327-365. | MR 58 #22059 | Zbl 0308.14003

[43 b] A. Ogus, On the formal neighborhood of a subvariety of projective space (to appear in Amer. J. Math.). | Zbl 0331.14002

[44] H.-J. Reiffen, Das Lemma von Poincaré für holomorphe Differentialformen auf Komplexen Räumen, Math. Zeit., 101 (1967), 269-284. | MR 36 #6647 | Zbl 0164.09401

[45] J.-E. Roos, Sur les foncteurs dérivés de lim. Applications. C. R. Acad. Sc. Paris, 252 (1961), 3702-3704. | MR 24 #A1938 | Zbl 0102.02501

[46] J.-P. Serre, Faisceaux algébriques cohérents (FAC), Annals of Math., 61 (1955), 197-278. | MR 16,953c | Zbl 0067.16201

[47] J.-P. Serre, Géométrie algébrique et géométrie analytique (GAGA), Ann. Inst. Fourier, 6 (1956), 1-42. | Numdam | MR 18,511a | Zbl 0075.30401

[48] E. H. Spanier, Algebraic Topology, McGraw-Hill, 1966. | MR 35 #1007 | Zbl 0145.43303

[49] 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. | Zbl 0276.32005