Abstract:Let $X$ be a closed symplectic manifold equipped with a Lagrangian torus fibration over a base $Q$. A construction first considered by Kontsevich and Soibelman produces from this data a rigid analytic space $Y$, which can be considered as a variant of the $T$-dual introduced by Strominger, Yau, and Zaslow. We prove that the Fukaya category of tautologically unobstructed graded Lagrangians in $X$ embeds fully faithfully in the derived category of (twisted) coherent sheaves on $Y$, under the technical assumption that $\pi _2(Q)$ vanishes (all known examples satisfy this assumption). The main new tool is the construction and computation of Floer cohomology groups of Lagrangian fibres equipped with topological infinite rank local systems that correspond, under mirror symmetry, to the affinoid rings introduced by Tate, equipped with their natural topologies as Banach algebras.

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中文翻译：

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无校正的同调镜像对称

摘要：令$X$ 是一个封闭辛流形，在基$Q$ 上装有拉格朗日环面纤维化。Kontsevich 和 Soibelman 首先考虑的构造从这些数据中产生了一个刚性分析空间 $Y$，它可以被认为是由 Strominger、Yau 和 Zaslow 引入的 $T$-对偶的变体。我们证明，在 $\pi _2(Q)$ 消失（所有已知例子满足这个假设）。主要的新工具是拉格朗日纤维的 Floer 上同调群的构建和计算，该群配备拓扑无限秩局部系统，在镜像对称下，对应于 Tate 引入的仿射环，

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