@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},
pages = {5--99},
year = {1975},
publisher = {Institut des Hautes Etudes Scientifiques},
volume = {45},
mrnumber = {55 #5633},
zbl = {0326.14004},
language = {en},
url = {https://www.numdam.org/item/PMIHES_1975__45__5_0/}
}
TY - JOUR AU - Hartshorne, Robin TI - On the de Rham cohomology of algebraic varieties JO - Publications Mathématiques de l'IHÉS PY - 1975 SP - 5 EP - 99 VL - 45 PB - Institut des Hautes Etudes Scientifiques UR - https://www.numdam.org/item/PMIHES_1975__45__5_0/ LA - en ID - PMIHES_1975__45__5_0 ER -
Hartshorne, Robin. On the de Rham cohomology of algebraic varieties. Publications Mathématiques de l'IHÉS, Tome 45 (1975), pp. 5-99. https://www.numdam.org/item/PMIHES_1975__45__5_0/
[1] , Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc., 85 (1957), 181-207. | Zbl | MR
[2] and , Integrals of the second kind on an algebraic variety, Ann. of Math., 62 (1955), 56-91. | Zbl | MR
[3] , Transplanting cohomology classes in complex projective space, Amer. J. Math., 92 (1970), 951-967. | Zbl | MR
[4] , Cohomologie p-cristalline des schémas, C. R. Acad. Sci. Paris, 269 (1969), 297-300 ; 357-360 ; 397-400. | Zbl | MR
[5] and , De Rham cohomology of an analytic space, Inv. Math., 7 (1969), 275-296. | Zbl | MR
[6] and , Homology theory for locally compact spaces, Mich. Math. J., 7 (1960), 137-159. | Zbl | MR
[7] and , Le théorème de Riemann-Roch, Bull. Soc. Math. France, 86 (1958), 97-136. | Zbl | MR | Numdam
[8] , Die Monodromie der isolierten Singularitäten von Hyperflächen, Manuscripta Math., 2 (1970), 103-161. | Zbl | MR
[9] , Anneaux de Chow et applications, Séminaire Chevalley, 1958.
[10] , Equations différentielles à points singuliers réguliers, Springer Lecture Notes, 163 (1970), 133 p. | Zbl | MR
[11] , Points de platitude d'un morphisme d'espaces analytiques complexes, Inv. Math., 4 (1967), 118-138. | Zbl | MR
[12] , Topologie algébrique et théorie des faisceaux, Hermann, Paris, 1958. | Zbl | MR
[13] , Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen, Publ. Math. I.H.E.S., 5 (1960), 5-64. | Zbl | Numdam
[14] , Sur quelques points d'algèbre homologique, Tohoku Math. J., 9 (1957), 119-221. | Zbl | MR
[15] , La théorie des classes de Chern, Bull. Soc. Math. France, 86 (1958), 137-154. | Zbl | MR | Numdam
[16] , On the De Rham cohomology of algebraic varieties, Publ. Math. I.H.E.S., 29 (1966), 95-103. | Zbl | MR | Numdam
[17] , Local Cohomology (LC), Springer Lecture Notes, 41 (1966). | Zbl | MR
[18] , 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. | Zbl | MR
[19] , Revêtements étales et groupe fondamental (SGA 1), Springer Lecture Notes, 224 (1971), 447 p. | Zbl | MR
[20] and , Elements de géométrie algébrique (EGA), Publ. Math. I.H.E.S., 4, 8, 11, 17, 20, 24, 28, 32 (1960-1967). | Numdam
[21] and , Analytic functions of several complex variables, Prentice-Hall, 1965. | Zbl | MR
[22] , Residues and Duality (RD), Springer Lecture Notes, 20 (1966). | Zbl | MR
[23] , Cohomological dimension of algebraic varieties, Annals of Math., 88 (1968), 403-450. | Zbl | MR
[24] , Ample subvarieties of algebraic varieties, Springer Lecture Notes, 156 (1970). | Zbl | MR
[25] , Cohomology of non-complete algebraic varieties, Compositio Math., 23 (1971), 257-264. | Zbl | MR | Numdam
[26] , Cohomology with compact supports for coherent sheaves on an algebraic variety, Math. Ann., 195 (1972), 199-207. | Zbl | MR
[27] , Algebraic De Rham cohomology, Manuscripta Math., 7 (1972), 125-140. | Zbl | MR
[28] , Topological conditions for smoothing algebraic singularities, Topology, 13 (1974), 241-253. | Zbl | MR
[29] and , Duality and the De Rham cohomology of infinitesimal neighborhoods, Invent. Math., 13 (1971), 97-124. | Zbl | MR
[30] , Resolution of singularities of an algebraic variety over a field of characteristic zero, I, II, Annals of Math., 79 (1964), 109-326. | Zbl | MR
[31] , and , Differential forms on regular affine algebras, Trans. Amer. Math. Soc., 102 (1962), 383-408. | Zbl | MR
[32] , Nilpotent connections and the monodromy theorem : applications of a result of Turrittin, Publ. Math. I.H.E.S., 39 (1970), 175-232. | Zbl | MR | Numdam
[33] , The regularity theorem in algebraic geometry, Proc. Int. Cong. Int. Cong. Math. in Nice, 1970, vol. 1, 437-443. | Zbl | MR
[34] and , On the differentiation of De Rham cohomology classes with respect to parameters, J. Math. Kyoto Univ., 8 (1968), 199-213. | Zbl | MR
[35] , Eine topologische Eigenschaft Steinscher Räume, Nachr. Akad. Wiss. Göttingen, 8 (1966). | Zbl
[36] , Note zu der Arbeit von J. Frisch " Points de platitude d'un morphisme d'espaces analytiques complexes ", Inv. Math., 4 (1967), 139-141. | Zbl | MR
[37] , Duality over complete local rings, Topology, 1 (1962), 213-235. | Zbl | MR
[38] , Formal cohomology II, Annals of Math., 88 (1968), 218-238. | Zbl
[39] , Finiteness of De Rham cohomology, Amer. J. Math., 94 (1972), 237-245. | Zbl | MR
[40] , Imbedding of an abstract variety in a complete variety, J. Math. Kyoto Univ., 2 (1962), 1-10. | Zbl | MR
[41] , A generalization of the embedding problem, J. Math. Kyoto Univ., 3 (1963), 89-102. | Zbl | MR
[42] , On the homology groups of Stein spaces, Inv. Math., 2 (1967), 377-385. | Zbl | MR
[43] , Local cohomological dimension of algebraic varieties, Thesis, Harvard, 1972. Added in proof : These results are published in two papers :
[43 a] , Local cohomological dimension of algebraic varieties, Annals of Math., 98 (1973), 327-365. | Zbl | MR
[43 b] , On the formal neighborhood of a subvariety of projective space (to appear in Amer. J. Math.). | Zbl
[44] , Das Lemma von Poincaré für holomorphe Differentialformen auf Komplexen Räumen, Math. Zeit., 101 (1967), 269-284. | Zbl | MR
[45] , Sur les foncteurs dérivés de lim. Applications. C. R. Acad. Sc. Paris, 252 (1961), 3702-3704. | Zbl | MR
[46] , Faisceaux algébriques cohérents (FAC), Annals of Math., 61 (1955), 197-278. | Zbl | MR
[47] , Géométrie algébrique et géométrie analytique (GAGA), Ann. Inst. Fourier, 6 (1956), 1-42. | Zbl | MR | Numdam
[48] , Algebraic Topology, McGraw-Hill, 1966. | Zbl | MR
[49] , 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






