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Portugaliae Mathematica

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Volume 74, Issue 2, 2017, pp. 149–159
DOI: 10.4171/PM/1997

Published online: 2017-11-10

Relative Riemann–Hilbert correspondence in dimension one

Teresa Monteiro Fernandes[1] and Claude Sabbah[2]

(1) Universidade de Lisboa, Portugal
(2) Ecole Polytechnique, Palaiseau, France

We prove that, in relative dimension one, the functor RH$^S$ constructed in a previous work ([9]) as a right quasi-inverse of the solution functor from the bounded derived category of relative $\mathcal D$-modules with regular holonomic cohomology to that of complexes with relative constructible cohomology satisfies the left quasi-inverse property in a generic sense.

Keywords: Relative holonomic $\mathcal D$-module, regularity, constructibility, adjoint functor

Fernandes Teresa Monteiro, Sabbah Claude: Relative Riemann–Hilbert correspondence in dimension one. Port. Math. 74 (2017), 149-159. doi: 10.4171/PM/1997