On a torsion analogue of the weight-monodromy conjecture

2020/08/27 by Ito, Kazuhiro
#14C25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary 11G25 #Secondary 14F20

paper · doi:10.48550/arxiv.2008.11905

Abstract

We formulate and study a torsion analogue of the weight-monodromy conjecture for a proper smooth scheme over a non-archimedean local field. We prove it for proper smooth schemes over equal characteristic non-archimedean local fields, abelian varieties, surfaces, varieties uniformized by Drinfeld upper half spaces, and set-theoretic complete intersections in toric varieties. In the equal characteristic case, our methods rely on an ultraproduct variant of Weil II established by Cadoret.

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