Weight-monodromy conjecture over equal characteristic local fields

The aim of this paper is to study certain properties of the weight spectral sequences of Rapoport-Zink by a specialization argument. By reducing to the case over finite fields previously treated by Deligne, we prove that the weight filtration and the monodromy filtration defined on the $l$-adic \'etale cohomology coincide, up to shift, for proper smooth varieties over equal characteristic local fields. We also prove that the weight spectral sequences degenerate at $E_2$ in any characteristic without using log geometry. Moreover, as an application, we give a modulo $p>0$ reduction proof of a Hodge analogue previously considered by Steenbrink.Comment: 12 pages, AMS LaTeX, revised version, to appear in the American Journal of Mathematic

Weight-monodromy conjecture for certain threefolds in mixed characteristic

The weight-monodromy conjecture claims the coincidence of the weight filtration and the monodromy filtration, up to shift, on the $l$-adic \'etale cohomology of a proper smooth variety over a complete discrete valuation field. Although it has been proved in some cases, the case of dimension $\geq 3$ in mixed characteristic is still open so far. The aim of this paper is to give a proof of the weight-monodromy conjecture for a threefold which has a projective strictly semistable model such that, for each irreducible component of the special fiber, the Picard number is equal to the second $l$-adic Betti number. Our proof is based on a careful analysis of the weight spectral sequence of Rapoport-Zink by the Hodge index theorem for surfaces. We also prove a $p$-adic analogue by using the weight spectral sequence of Mokrane.Comment: 16 pages, Example 1.3 added, minor modifications, to appear in IMR

Plan of advanced satellite communication experiments using ETS-6

In 1992, an Engineering Test Satellite 6 is scheduled to be launched by an H-2 rocket. The missions of ETS-6 are to establish basic technologies of inter-satellite communications using S-band, millimeter waves and optical beams and of fixed and mobile satellite communications using multibeam antenna on board the satellite. A plan of the experiments is introduced