It has been proven by Serre, Larsen–Pink and Chin, that over a smooth curve over a finite field, the monodromy groups of compatible semi-simple pure lisse sheaves have “the same” \(\pi _0\) and neutral component. We generalize their results to compatible systems of semi-simple lisse sheaves and overconvergent F-isocrystals over arbitrary smooth varieties. For this purpose, we extend the theorem of Serre and Chin on Frobenius tori to overconvergent F-isocrystals. To put our results into perspective, we briefly survey recent developments of the theory of lisse sheaves and overconvergent F-isocrystals. We use the Tannakian formalism to make explicit the similarities between the two types of coefficient objects.

中文翻译：

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lisse滑轮和过度收敛的F-异晶体的单峰群

Serre，Larsen-Pink和Chin已证明，在有限域上的平滑曲线上，兼容的半简单纯lisse滑轮的单峰组具有“相同” \（\ pi _0 \）和中性成分。我们将它们的结果推广到半简单lisse滑轮和任意会聚光滑品种上的过会聚F-异晶的兼容系统。为此，我们将Frobenius花托上的Serre和Chin定理扩展到了过度收敛的F-等晶体。为了使我们的结果更直观，我们简要概述了lisse滑轮和过会聚的F-异晶体理论的最新进展。我们使用Tannakian形式主义来明确表明两种系数对象之间的相似性。