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arXiv · 0907.2331

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

Eva Viehmann
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Abstract

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

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Eva Viehmann. 2013-09-26. Truncations of level 1 of elements in the loop group of a reductive group. https://arxiv.org/abs/0907.2331

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