Potentially good reduction of Barsotti-Tate groups |
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Authors: | Tong Liu |
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Institution: | Université de Paris-Sud, Mathématiques, Bâtiment 425, 91405 Orsay cedex, France |
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Abstract: | Let R be a complete discrete valuation ring of mixed characteristic (0,p) with perfect residue field, K the fraction field of R. Suppose G is a Barsotti-Tate group (p-divisible group) defined over K which acquires good reduction over a finite extension K′ of K. We prove that there exists a constant c?2 which depends on the absolute ramification index e(K′/Qp) and the height of G such that G has good reduction over K if and only if Gpc] can be extended to a finite flat group scheme over R. For abelian varieties with potentially good reduction, this result generalizes Grothendieck's “p-adic Néron-Ogg-Shafarevich criterion” to finite level. We use methods that can be generalized to study semi-stable p-adic Galois representations with general Hodge-Tate weights, and in particular leads to a proof of a conjecture of Fontaine and gives a constant c as above that is independent of the height of G. |
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Keywords: | primary 14F30 14L05 |
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