Monodromy Filtration and Positivity

2000/06/21 by Morihiko Saito, Saito, Morihiko · 1 citation
Mathematics · #14C25 #14F20 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14C25 #msc:14F20

paper · pdf · doi:10.48550/arxiv.math/0006162

19 pages, example added

openalex publication_date 2000/06/21 · arxiv created 2003/09/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Deligne's conjecture on the monodromy weight filtration on the nearby cycles in the mixed characteristic case, and reduce it to the nondegeneracy of certain pairings in the semistable case. We also prove a related conjecture of Rapoport and Zink which uses only the image of the Cech restriction morphism, if Deligne's conjecture holds for a general hyperplane section. In general we show that Deligne's conjecture is true if the standard conjectures hold.

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• Limits of weight filtrations and limits of slope filtrations on\n infinitesimal cohomologies in mixed characteristics I

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