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arXiv · 2502.04148

Hodge microsheaves on cotangent bundles and plumbings

Tatsuki Kuwagaki·Takahiro Saito
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Abstract

We introduce and study the category of Hodge microsheaves which is a Hodge-version of the category of microsheaves for a certain class of holomorphic exact symplectic manifolds. We then study Hodge-theoretic version of wrapped sheaves and discuss applications in topology and representation theory. Namely, we study (1) Hain's Hodge structures on the cohomology of based loop spaces of algebraic varieties, and (2) the Koszul duality of Ginzburg algebras by Etg\"u-Lekili from a mixed geometric perspective.

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Tatsuki Kuwagaki, Takahiro Saito. 2025-02-06. Hodge microsheaves on cotangent bundles and plumbings. https://arxiv.org/abs/2502.04148

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