论文标题
相对复杂方案上的常规连接
Regular-singular connections on relative complex schemes
论文作者
论文摘要
Deligne著名的“ Riemann--Hilbert信函”涉及平滑复杂的代数品种和常规的可融合连接的基本组的表示。在这项工作中，我们展示了如何在ring $ r = \ mathbb c [[[t_1，\ ldots，t_r]]/i $的范围内的平滑方案$ x $的情况下得出类似的说明。在信函的一侧，我们对特殊光纤基本组的$ r $ tomodules表示了表示，另一方面，我们有某些可集成的$ r $ $ - 连接，可以承认对数模型。然后将通信应用于$ \ Mathbb C [[t]] $ - 连接的差分galois组的明确示例。
Deligne's celebrated "Riemann--Hilbert correspondence" relates representations of the fundamental group of a smooth complex algebraic variety and regular-singular integrable connections. In this work, we show how to arrive at a similar statement in the case of a smooth scheme $X$ over the spectrum of a ring $R=\mathbb C[[t_1,\ldots, t_r]]/I$. On one side of the correspondence we have representations on $R$-modules of the fundamental group of the special fibre, and on the other we have certain integrable $R$-connections admitting logarithmic models. The correspondence is then applied to give explicit examples of differential Galois groups of $\mathbb C[[t]]$--connections.
