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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)

MSC:

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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