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<p>We establish an explicit relative Riemann–Hilbert correspondence for Alexander complexes (also known as Sabbah specialization complexes) using relative regular holonomic <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathscr {D}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">D</mi> </math></EquationSource> </InlineEquation>-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.</p>

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Riemann–Hilbert Correspondence for Alexander Complexes

  • 期刊论文

  • 发表日期：

    2026年6月17日

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  • Lei Wu

摘要

We establish an explicit relative Riemann–Hilbert correspondence for Alexander complexes (also known as Sabbah specialization complexes) using relative regular holonomic \({\mathscr {D}}\) 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.