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<p>Motivated by the work of Kontsevich–Soibelman on the comparison of isomorphisms conjecture for closed algebraic 1-forms, we establish a Riemann–Hilbert correspondence of Deligne–Malgrange type. As an application, we prove a variant of the comparison of isomorphisms theorem for a simple class of algebraic 1-forms on complex curves.</p>

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A Riemann–Hilbert correspondence for cohomology theories of closed 1-forms

  • 期刊论文

  • 发表日期：

    2026年7月7日

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  • Yota Shamoto

摘要

Motivated by the work of Kontsevich–Soibelman on the comparison of isomorphisms conjecture for closed algebraic 1-forms, we establish a Riemann–Hilbert correspondence of Deligne–Malgrange type. As an application, we prove a variant of the comparison of isomorphisms theorem for a simple class of algebraic 1-forms on complex curves.