Newton strata in the loop group of a reductive group

2010/05/31 by Eva Viehmann, Viehmann, Eva
Mathematics · #14L05 (Secondary) #20G25 (Primary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR #msc:14L05 #msc:20G25

paper · pdf · doi:10.48550/arxiv.1005.5725

15 pages; exposition improved, minor corrections

arxiv created 2011/05/04 · arxiv updated 2011/05/05

Abstract

We generalize purity of the Newton stratification to purity for a single break point of the Newton point in the context of local G-shtukas respectively of elements of the loop group of a reductive group. As an application we prove that elements of the loop group bounded by a given dominant coweight satisfy a generalization of Grothendieck's conjecture on deformations of p-divisible groups with given Newton polygons.

Related

• Truncations of level 1 of elements in the loop group of a reductive group
• Dimensions of Newton strata in the adjoint quotient of reductive groups
• Steinberg's cross-section of Newton strata
• A geometric interpretation of Newton strata
• Generic Newton points and the Newton poset in Iwahori double cosets