Overholonomicity of overconvergent $F$-isocrystals over smooth varieties

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.

Authors

Daniel Caro

Laboratoire de Mathématiques Nicolas Oresme
Université de Caen
Campus 2
14032 Caen cedex
France

Nobuo Tsuzuki

Mathematical Institute
Tohoku University
Sendai 980-8576
Japan