Abstract
We prove the overholonomicity of overconvergent $F$-isocrystals over
smooth varieties. This implies that the notions of overholonomicity and devissability in overconvergent $F$-isocrystals are equivalent. Then the overholonomicity is stable under tensor products. So, the overholonomicity gives a $p$-adic cohomology stable under Grothendieck’s cohomological operations.
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AUTHOR = {Andr{é},
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SERIES = {Progr. Math.},
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@misc{caro-stab-prod-tens,
author={Caro, Daniel},
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URL = {http://www.math.unicaen.fr/~caro/#prepublication},
YEAR={2007},
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AUTHOR = {Caro, Daniel},
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JOURNAL = {Ann. Sci. École Norm. Supér.},
FJOURNAL = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
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VOLUME = {16},
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NUMBER = {1},
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ISSN = {1340-5705},
MRCLASS = {14F30 (14F10 14F40)},
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ZBLNUMBER = {1213.14041},
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AUTHOR = {Kedlaya, Kiran S.},
TITLE = {Full faithfulness for overconvergent {$F$}-isocrystals},
BOOKTITLE = {Geometric Aspects of {D}work Theory. {V}ol. {I},
{II}},
PAGES = {819--835},
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}