Codimensions of Newton strata for SL₃(F) in the Iwahori case

摘要

We study the Newton stratification on SL ₃(F), where F is a Laurent power series field. We provide a formula for the codimensions of the Newton strata inside each component of the affine Bruhat decomposition on SL ₃(F). These calculations are related to the study of certain affine Deligne–Lusztig varieties. In particular, we describe a method for determining which of these varieties is non-empty in the case of SL ₃(F). Keywords Newton polygon - Newton stratification - Isocrystal - Affine Bruhat decomposition - Affine Deligne–Lusztig variety - Frobenius-linear characteristic polynomial Mathematics Subject Classification (2000) Primary 20G25 - Secondary 14L05