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Abstract: We generalize the notion of Ekedahl-Oort strata to elements in the loop groupof any connected reductive group, and call the resulting discrete invariant thetruncation of level 1 of the element. We give conditions for the Newton pointsoccurring among the elements of a given truncation of level 1 and especiallyfor the generic Newton point in a given truncation stratum. We prove thattruncation strata are locally closed and give a description of the closure ofeach stratum. We also translate our results back to the original Ekedahl-Oortstratification of the reduction modulo p of Shimura varieties.



Author: Eva Viehmann

Source: https://arxiv.org/



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