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Breuil-Kisin windows and the Ekedahl-Oort stratification of Shimura varieties
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2018-01-01 12:13  »ª¶«Ê¦·¶´óÑ§

By constructing (non-canonical) deformations for the associated p-divisible groups of the special fibre S of a Shimura variety, we manage to construct a morphism from S to some quotient sheaf of the loop group associated with S. We show that the geometric fibre of this morphism gives back the Ekedahl-Oort (EO) strata of S: this also gives a conceptual interpretation of Viehmann's new invariant "elements of truncation of level one". I will recall the EO stratification of Shimura varieties (of good reduction) and the classification of p-divisible groups in terms of filtered Breuil-Kisin modules (or Breuil-Kisin windows, in my term), and then present the main results in a precise form.

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