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