We prove the p-curvature conjecture for rank two vector bundles with connection on generic curves. Our ingredients include new deformation techniques for vector bundles with vanishing p-curvatures on families of varieties, as well as topological criteria for finiteness of surface group representations in terms of simple loops and pairs of pants.

中文翻译：

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秩2个p上通用的曲线-curvature猜想

我们证明了具有通用曲线连接的秩二向量丛的p曲率猜想。我们的成分包括新的变形技术，用于在变体家族上具有消失的p曲率的向量丛，以及根据简单环和裤子的表面群表示有限性的拓扑标准。