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arXiv · 1711.06669

The monodromy groups of lisse sheaves and overconvergent $F$-isocrystals

Marco D'Addezio
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Abstract

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" $π_0$ 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.

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Marco D'Addezio. 2020-05-27. The monodromy groups of lisse sheaves and overconvergent $F$-isocrystals. https://doi.org/10.1007/s00029-020-00569-3

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