BENOIT TRIHAN FABIEN

We show that the Dieudonne crystal associated to a Barsotti-Tate group with potentially semistable reduction over a smooth curve is overconvergent. As a corollary, we obtain the rationality of the L-function associated to this group.

Let X be a proper smooth curve over a perfect field of characteristic p > 0 and U an open dense subscheme of X. We prove that convergent F-isocrystals on U are overconvergent under the condition that they are overconvergent at each point in X/U. U...