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A Fourier transform for sheaves on real tori. II: Relative theory. (English) Zbl 1071.14515
Summary: If \(X\) is a symplectic family of Lagrangian tori, the dual family \(\widehat X\) has a natural complex structure. We define, for any dimension of \(X\), a Fourier transform which yields a bijective correspondence between local systems supported on Lagrangian submanifolds of \(X\) and holomorphic vector bundles supported on complex subvarieties of \(\widehat X\) (suitable conditions being verified on both sides).

MSC:
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
32Q25 Calabi-Yau theory (complex-analytic aspects)
58J22 Exotic index theories on manifolds
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