p-adic Hodge theory of de Rham local systems, I: Newton polygon and monodromy

Abstract

We prove that the relative p-adic monodromy theorem holds over a dense open subset. Moreover, we establish the equivalence of the following two statements: the local constancy of the Newton polygon function associated with a de Rham local system around rank-1 points, and the relative p-adic monodromy theorem near rank-1 points. We demonstrate how to extend the relative p-adic monodromy conjecture from the neighborhood of rank-1 points to the entire interiors of Newton partitions. Finally, we verify a conjecture of Howe-Klevdal concerning the potential good reduction of admissible pairs arising from variant of p-adic Hodge structures.

72 pages, 1 figure. The main result is now formulated in terms of de Jong coverings. The exposition has been improved, particularly in Section 5.3. Comments are welcome