The Čech Filtration and Monodromy in Log Crystalline Cohomology

For a strictly semistable log scheme Y over a perfect field k of characteristic p we investigate the canonical Čech spectral sequence (C)T abutting the Hyodo-Kato (log crystalline) cohomologyH∗ crys(Y/T )Q of Y and beginning with the log convergent cohomology of its various component intersections Y i. We compare the filtration on H∗ crys(Y/T )Q arising from (C)T with the monodromy operator N on H∗ crys(Y/T )Q. We also express N through residue maps and study relations with singular cohomology. If Y lifts to a proper strictly semistable (formal) scheme X over a finite totally ramified extension of W (k), with generic fibre XK , we obtain results on how the simplicial structure of Xan K (as analytic space) is reflected in H ∗ dR(XK) = H ∗ dR(X an K ).