Weight-monodromy conjecture for certain threefolds in mixed characteristic
Tetsushi Ito
Abstract
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 ≥ 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.
Create a lesson
Related papers
An Infinite Family of Apéry-like Recurrences for Euler's Constant
Rotem Kalisch, Tali Monderer, Elyasheev Leibtag et al.
On the saturability of p-adic Lie groups
Casey Perdue
On Divisor Function Polynomials and Dirichlet Series
Martin N. Huxley, Matthew C. Lettington, Karl Michael Schmidt
On a conjecture on Romanoff type representations
Xiao-Hui Yan
Regularization of a Divergent Arithmetic Product via the Asymptotic Monoid: The Case of (-1)ω(n)
A. Alvarez Cruz, E. A. Alvarez Gutierrez
Appell Sequences in Analytic Number Theory: Shifted Expansions and Dirichlet L-Functions
Abdelmejid Bayad