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.
[Kuo23] Christopher Kuo
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Hodge microsheaves on cotangent bundles and plumbings
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.