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<p>In this paper, we reprove the Riemann–Hilbert correspondence for regular holonomic <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {D}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">D</mi> </math></EquationSource> </InlineEquation>-modules of Kashiwara (Publ. Res. Inst. Math. Sci. <b>20</b>(2), 319–365, 1984) (see also Mebkhout (Compositio Math. 51(1), 63–88, 1984)) by using the irregular Riemann–Hilbert correspondence of D’Agnolo (Publ. Math. Inst. Hautes Études Sci. <b>123</b>(1), 69–197, 2016). Moreover, we also reprove the algebraic one by the same argument. For this purpose, we study <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb {C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">C</mi> </math></EquationSource> </InlineEquation>-constructible enhanced ind-sheaves of Ito (Tsukuba J. of Math. <b>44</b>(1), 155–201, 2020), Ito (Sem. Mat. Univ. Padova. <b>149</b>(1), 45–81, 2021) in more detail.</p>

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Another Proof of the Riemann–Hilbert Correspondence for Regular Holonomic \(\mathcal {D}\)-Modules

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  • 发表日期：

    2026年4月28日

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  • Yohei ITO

摘要

In this paper, we reprove the Riemann–Hilbert correspondence for regular holonomic \(\mathcal {D}\) D -modules of Kashiwara (Publ. Res. Inst. Math. Sci. 20(2), 319–365, 1984) (see also Mebkhout (Compositio Math. 51(1), 63–88, 1984)) by using the irregular Riemann–Hilbert correspondence of D’Agnolo (Publ. Math. Inst. Hautes Études Sci. 123(1), 69–197, 2016). Moreover, we also reprove the algebraic one by the same argument. For this purpose, we study \(\mathbb {C}\) C -constructible enhanced ind-sheaves of Ito (Tsukuba J. of Math. 44(1), 155–201, 2020), Ito (Sem. Mat. Univ. Padova. 149(1), 45–81, 2021) in more detail.