Abstract:We define study privileged local systems on a smooth quasi-projective complex variety $X$ with fixed quasi-unipotent monodromies around a boundary divisor. The notion is a generalization of Katz' physical rigidity on an open of $\mathbb P^1$. It is defined in any dimension and
includes non-rigid local systems. In the latter case, Katz used the \emph{middle convolution} procedure to classify all physically local systems and derived several consequences such as the $p$-curvature conjecture for local systems of this type. We present a new proof, which avoids the use of middle convolution. This yields examples in higher dimension of local systems which verify the $p$-curvature conjecture.
From: Hélène Esnault [view email]
[v1]
Mon, 15 Jun 2026 15:49:55 UTC (19 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。