Weights in cohomology groups arising from hyperplane arrangements
HTML articles powered by AMS MathViewer
- by Minhyong Kim
- Proc. Amer. Math. Soc. 120 (1994), 697-703
- DOI: https://doi.org/10.1090/S0002-9939-1994-1179589-0
- PDF | Request permission
Abstract:
The formalism of weights allows very simple analysis of the cohomology of hyperplane complements in a uniform fashion for different cohomology theories. An $l$-adic analogue of Arnold’s conjecture on the torsion-freeness of these cohomology groups is one of the consequences.References
- Pierre Deligne, Théorie de Hodge. I, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 425–430 (French). MR 0441965 —, Théories de Hodge. II, III, Inst. Hautes Études Sci. Publ. Math 40 (1972), 5-57; 44 (1975), 6-77.
- Pierre Deligne, Poids dans la cohomologie des variétés algébriques, Proceedings of the International Congress of Mathematicians (Vancouver, B.C., 1974) Canad. Math. Congress, Montreal, Que., 1975, pp. 79–85. MR 0432648
- Fouad El Zein, Mixed Hodge structures, Trans. Amer. Math. Soc. 275 (1983), no. 1, 71–106. MR 678337, DOI 10.1090/S0002-9947-1983-0678337-5
- Luc Illusie, Cohomologie de de Rham et cohomologie étale $p$-adique (d’après G. Faltings, J.-M. Fontaine et al.), Astérisque 189-190 (1990), Exp. No. 726, 325–374 (French). Séminaire Bourbaki, Vol. 1989/90. MR 1099881
- Minhyong Kim, On Poincaré polynomials for hyperplane arrangements in positive characteristic, Comm. Algebra 21 (1993), no. 4, 1337–1346. MR 1209932, DOI 10.1080/00927879308824622
- James S. Milne, Étale cohomology, Princeton Mathematical Series, No. 33, Princeton University Press, Princeton, N.J., 1980. MR 559531
- Peter Orlik and Louis Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math. 56 (1980), no. 2, 167–189. MR 558866, DOI 10.1007/BF01392549
- Peter Orlik and Hiroaki Terao, Arrangements of hyperplanes, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 300, Springer-Verlag, Berlin, 1992. MR 1217488, DOI 10.1007/978-3-662-02772-1
- Tammo tom Dieck, Transformation groups, De Gruyter Studies in Mathematics, vol. 8, Walter de Gruyter & Co., Berlin, 1987. MR 889050, DOI 10.1515/9783110858372.312
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 697-703
- MSC: Primary 14F20; Secondary 14C30, 52B30
- DOI: https://doi.org/10.1090/S0002-9939-1994-1179589-0
- MathSciNet review: 1179589