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I will recall Kashiwara's conjugation functor from the derived category of regular holonomic D-modules over a complex manifold to the derived category of regular holonomic D-modules on the complex conjugate manifold \bar{X}, which he proved to be an equivalence of categories thanks to the Riemann-Hilbert correspondence. Next I will construct, thanks to the relative Riemann-Hilbert correspondence obtained with Fiorot and Sabbah, a relative conjugation functor from the derived category of relative regular holonomic D-modules over a product XxS to the derived category of relative regular holonomic D-modules on \bar{X} x S and show that this conjugation functor is an equivalence of categories. In both situations the main tool is the sheaf of distributions on X (respectively on XxS) whose surprising importance will be exemplified.
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