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The microlocal Riemann-Hilbert correspondence for complex contact manifolds

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arxiv 2406.16222 v2 pith:CACUDZIO submitted 2024-06-23 math.SG math.AGmath.RT

Laurent Côté , Christopher Kuo , David Nadler , Vivek Shende This is my paper · ORCID
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Kashiwara showed in 1996 that the categories of microlocalized D-modules can be canonically glued to give a sheaf of categories over a complex contact manifold. Much more recently, and by rather different considerations, we constructed a canonical notion of perverse microsheaves on the same class of spaces. Here we provide a Riemann-Hilbert correspondence.

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  1. Hodge microsheaves on cotangent bundles and plumbings

    math.AG 2025-02 conditional novelty 8.0 of 10

    A new category of Hodge microsheaves is defined via gluing mixed Hodge modules, and it reproduces Hain's loop Hodge structure on P^n and gives a mixed-geometric proof of Etgü–Lekili Koszul duality.

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