Perverse microsheaves

Laurent Côté, Christopher Kuo, David Nadler, Vivek Shende

Research output: Working paperResearch

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Abstract

An exact complex symplectic manifold carries a sheaf of stable categories, locally equivalent to a microlocalization of a category of constructible sheaves. This sheaf of categories admits a t-structure, whose heart is locally equivalent to a microlocalization of a category of perverse sheaves. The abelian category of local systems on a spin conic complex Lagrangian embeds fully faithfully in the heart. The sheaf of homs between two objects in the heart is itself a perverse sheaf, shifted by half the dimension of the ambient manifold. Analogous results hold for complex contact manifolds. The correspondence between microsheaves and Fukaya categories yields t-structures on Fukaya categories of conic complex symplectic manifolds, with holomorphic Lagrangians in the heart.
Original languageEnglish
PublisherarXiv.org
Number of pages25
DOIs
Publication statusPublished - 26. Sept 2022

Keywords

  • math.SG
  • math.AG
  • math.RT

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