Overholonomicity of overconvergent $F$-isocrystals over smooth varieties

Details Overholonomicity of overconvergent $F$-isocrystals over smooth varieties Overholonomicity of overconvergent $F$-isocrystals over smooth varieties

2008-03-14

arxiv.org/abs/0803.2105v1

Mathematics

Algebraic Geometry

41 pages

Scientific paper

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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