Homology for irregular connections. (English) Zbl 1075.14016

Author’s abstract: Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. The process of integrating forms over chains is compatible with homological and cohomological equivalences and defines a perfect pairing between the de Rham cohomology with values in the connection and homology with values in the dual connection.
Reviewer: Tan VoVan (Boston)


14F40 de Rham cohomology and algebraic geometry
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
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[1] P. Deligne, Équations Différentielles à Points Singuliers Réguliers. Lecture Notes in Mathematics 163, Springer Verlag, 1970. · Zbl 0244.14004
[2] N. Kachi, K. Matsumoro, M. Mihara, The perfectness of the intersection pairings for twisted cohomology and homology groups with respect to rational \(1\)-forms. Kyushu J. Math. 53 (1999), 163-188. · Zbl 0933.14009
[3] G. Laumon, Transformation de Fourier, constantes d’équations fonctionnelles, et conjecture de Weil. Publ. Math. IHES 65 (1987), 131-210. · Zbl 0641.14009
[4] B. Malgrange, Équations Différentielles à Coefficients Polynomiaux. Progress in Math. 96, Birkhäuser Verlag, 1991. · Zbl 0764.32001
[5] B. Malgrange, Remarques sur les équations différentielles à points singuliers irréguliers. Springer Lecture Notes in Mathematics 712 (1979), 77-86. · Zbl 0423.32014
[6] B. Malgrange, Sur les points singuliers des équations différentielles. L’Enseignement mathématique, t. 20, 1-2 (1974), 147-176. · Zbl 0299.34011
[7] T. Saito, T. Terasoma, Determinant of Period Integrals. J. AMS 10 (1997), 865-937. · Zbl 0956.14005
[8] T. Terasoma, Confluent Hypergeometric Functions and Wild Ramification. Journ. of Algebra 185 (1996), 1-18. · Zbl 0873.12004
[9] T. Terasoma, A Product Formula for Period Integrals. Math. Ann. 298 (1994), 577-589. · Zbl 0811.32014
[10] G.N. Watson, E.T. Whittaker, A Course of modern Analysis. Cambridge University Press, 1965. · JFM 45.0433.02
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