Truncations of level 1 of elements in the loop group of a reductive\n group

2009/07/14 by Eva Viehmann, Viehmann, Eva · 2 citations
Mathematics · Physics and Astronomy · #14G35 #14K10 #20G25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0907.2331

openalex publication_date 2009/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the notion of Ekedahl-Oort strata to elements in the loop group\nof any connected reductive group, and call the resulting discrete invariant the\ntruncation of level 1 of the element. We give conditions for the Newton points\noccurring among the elements of a given truncation of level 1 and especially\nfor the generic Newton point in a given truncation stratum. We prove that\ntruncation strata are locally closed and give a description of the closure of\neach stratum. We also translate our results back to the original Ekedahl-Oort\nstratification of the reduction modulo p of Shimura varieties.\n

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