  We establish a Riemann-Hilbert correspondence for Alexander complexes (also
known as Sabbah specialization complexes) by using relative holonomic $\mathscr
D$-modules in an equivariant way, which particularly gives a "global" approach
to the correspondence 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.
