Abstract
AbstractIt 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” $$\pi _0$$
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.
Funder
Max Planck Institute for Mathematics
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy,General Mathematics
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