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
Reference45 articles.
1. Abe, T.: Langlands program for $$p$$-adic coefficients and the petits camarades conjecture. Math. J. Reine Angew. 739, 59–69 (2015)
2. Abe, T.: Langlands correspondence for isocrystals and the existence of crystalline companions for curves. J. Am. Math. Soc. 31, 921–1057 (2018)
3. Abe, T., Caro, D.: On Beilinson’s equivalence for $$p$$-adic cohomology. Selecta Math. 24, 591–608 (2018)
4. Abe, T., Esnault, H.: A Lefschetz theorem for overconvergent isocrystals with Frobenius structure. Ann. Sci. Èc. Norm. Supér. 52, 1243–1264 (2019)
5. Ambrosi, E., D’Addezio, M.: Maximal tori of monodromy groups of $$F$$-isocrystals and an application to abelian varieties. arXiv:1811.08423 (2018)
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