Weight-monodromy conjecture for certain threefolds in mixed characteristic
| dc.creator | Ito, Tetsushi | |
| dc.date | 2002-12-09 | |
| dc.date | 2003-07-31 | |
| dc.date.accessioned | 2026-07-07T04:53:37Z | |
| dc.date.available | 2026-07-07T04:53:37Z | |
| dc.description | The weight-monodromy conjecture claims the coincidence of the weight filtration and the monodromy filtration, up to shift, on the $l$-adic étale 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. | |
| dc.description | 16 pages, Example 1.3 added, minor modifications, to appear in IMRN | |
| dc.identifier | https://arxiv.org/abs/math/0212109 | |
| dc.identifier | http://arxiv.org/abs/math/0212109 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65921 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G25; 14G20; 14F20; 14D07 | |
| dc.title | Weight-monodromy conjecture for certain threefolds in mixed characteristic | |
| dc.type | text |