2018
DOI: 10.1007/s10240-018-0100-0
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Integral models of Shimura varieties with parahoric level structure

Abstract: For a prime p > 2, we construct integral models over p for Shimura varieties with parahoric level structure, attached to Shimura data (G, X) of abelian type, such that G splits over a tamely ramified extension of Qp. The local structure of these integral models is related to certain "local models", which are defined group theoretically. Under some additional assumptions, we show that these integral models satisfy a conjecture of Kottwitz which gives an explicit description for the trace of Frobenius action on … Show more

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Cited by 63 publications
(139 citation statements)
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References 55 publications
(115 reference statements)
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“…Then the model [46], and under the assumption p ∤ |π 1 (G der )|. The statement above is for the modified local models of this paper and can be deduced by the results in [30]. Part (b) follows from [30, Thm.…”
Section: Shimura Varietiesmentioning
confidence: 91%
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“…Then the model [46], and under the assumption p ∤ |π 1 (G der )|. The statement above is for the modified local models of this paper and can be deduced by the results in [30]. Part (b) follows from [30, Thm.…”
Section: Shimura Varietiesmentioning
confidence: 91%
“…is a bijection. b) ( [30]) Assume that (G, X) is of Hodge type, that K is the stabilizer of a point in the Bruhat-Tits building of G, and that p does not divide |π 1 (G der )|. Then the model [46], and under the assumption p ∤ |π 1 (G der )|.…”
Section: Shimura Varietiesmentioning
confidence: 99%
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“…This is deduced in [Ki 2, 3.4.13] from Deligne's results [De 2], except for the claim in (2) that (G, X) can be chosen so that Z G is a torus, and the final claim in (3) that (G, X) may be chosen so that E(G, X) p = E(G ad , X ad ) p . That (G, X) may be chosen to satisfy the former condition is shown in [KP,4.6.22]. The construction of (G, X) in (2) uses [De 2, 2.3.10].…”
Section: Proofmentioning
confidence: 99%
“…In joint work with Rapoport [32], we purposed an axiomatic approach to the study of these characteristic subsets in a general Shimura variety. We formulated five axioms, based on the existence of integral models of Shimura varieties (which have been established in various cases by the work of Rapoport and Zink [66], Kisin and Pappas [40]), the existence of the following commutative diagram and some compatibility conditions:…”
Section: Some Applications To Shimura Varietiesmentioning
confidence: 99%