A converse to Mazur's inequality for split classical groups

2002/11/20 by Catherine Leigh, Leigh, Catherine
Mathematics · #11S25 #14F30 #14L05 #20G25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11S25 #msc:14F30 #msc:14L05 #msc:20G25

paper · pdf · doi:10.48550/arxiv.math/0211327

16 pages

arxiv created 2002/11/20 · arxiv updated 2009/11/30

Abstract

Given a lattice in an isocrystal, Mazur's inequality states that the Newton point of the isocrystal is less than or equal to the invariant measuring the relative position of the lattice and its transform under Frobenius. Conversely, it is known that any potential invariant allowed by Mazur's inequality actually arises from some lattice. These can be regarded as statements about the group GL_n. This paper proves an analogous converse theorem for all split classical groups.

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