On the p-adic local invariant cycle theorem

الأصل · EN

For a proper, flat, generically smooth scheme X over a complete DVR with finite residue field of characteristic p, we define a specialization morphism from the rigid cohomology of the geometric special fibre to Dcrys of the p-adic étale cohomology of the geometric generic fibre, and we make a conjecture ("p-adic local invariant cycle theorem") that describes the behavior of this map for regular X, analogous to the situation in l-adic étale cohomology for l≠ p. Our main result is that, if X has semistable reduction, this specialization map induces an isomorphism on the slope [0,1)-part.