Group schemes with additional structures and Weyl group cosets

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Algebraic zip data (2010, result): “s which pertain to the study of modulo preductions of Fcrystals with additional structure that show up in the study of special ﬁbers of good integral models of Shimura varieties of Hodge type Moonen ([Moo]) and, more generally, Vasiu ([Vas]) have obtained similar classiﬁcation results. In these case”
Strata Hasse invariants, Hecke algebras and Galois representations (2015, methodology): “e parametrized strata combinatorially by "elementary sequences". Later on, Moonen used the canonical ﬁltration of a BT1 with PEL-structure to give a group-theoretical classiﬁcation of these [81]. He described isomorphism classes of BT1’s over an algebraically closed ﬁeld kof characteristic”
$F$-zips with additional structure (2012, background): “This was first proved by Moonen in [15].”
Serre-Tate theory for moduli spaces of PEL type (2002, methodology): “— In [22] we have given two versions of the above theorem: the result as stated here, and a version working with the possibly non-connected group G.”
Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type (2013, methodology): “I would also like to thank Ben Moonen, Torsten Wedhorn, Daniel Wortmann as well as the referees for corrections and helpful remarks.”