Weight-monodromy conjecture over equal characteristic local fields

2003/08/14 by Tetsushi Ito, Ito, Tetsushi · 2 citations
Computer Science · Mathematics · #14D07 #14F20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Primary: 11G25 #Secondary: 14G20 #math.AG #math.NT #msc:11G25 #msc:14D07 #msc:14F20 #msc:14G20

paper · pdf · doi:10.48550/arxiv.math/0308141

12 pages, AMS LaTeX, revised version, to appear in the American Journal of Mathematics

openalex publication_date 2003/08/14 · arxiv created 2005/01/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 étale cohomology coincide, up to shift, for proper smooth varieties over equal characteristic local fields. We also prove that the weight spectral sequences degenerate at E₂ 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.

Citations

• Good Reduction of Abelian Varieties

Cited by

• Logarithmic geometry and Frobenius, II
• A Weight Structure on Rigid Analytic Motives over a Field

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