On the etale cohomology of algebraic varieties with totally degenerate reduction over p-adic fields

2003/06/06 by Wayne Raskind, Raskind, Wayne, Xavier Xarles +1
Computer Science · Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14F20 #14F30 (primary) and 14G20 (secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14F20 #msc:14F30 #msc:14G20

paper · pdf · doi:10.48550/arxiv.math/0306123

29 pages This and math.AG/0601401 replace math.AG/0306123

openalex publication_date 2003/06/06 · arxiv created 2006/01/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a finite extension of Q_p and X a smooth projective variety over K. We define the notion of totally degenerate reduction of such an X and the associated Chow complexes of the special fibre of a suitable regular proper model of X over the ring of integers of K. If X has such reduction, we then show that for all l, the Q_l-adic etale cohomology of X has a filtration whose graded quotients are isomorphic, as Galois modules, to the tensor product of a finite dimensional Q-vector space (with a finite unramified action of Galois) with twists of Q_l by the cyclotomic character.

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