Riemann–Hilbert Correspondence for Alexander Complexes

Abstract

We establish an explicit relative Riemann–Hilbert correspondence for Alexander complexes (also known as Sabbah specialization complexes) using relative regular holonomic ${\mathscr {D}}$-modules in an equivariant way, generalizing a classical result of Kashiwara and Malgrange for Deligne’s nearby cycles. Using the correspondence and zero loci of Bernstein–Sato ideals, we obtain a formula for the relative support of the Alexander complexes.

Keywords

Relative Riemann–Hilbert correspondence / Nearby cycles / Bernstein–Sato ideals / 14F10 / 13N10 / 32C38 / 32S60 / 32S55 / 14F43 / 14L30

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