On the Deformation of a Barsotti-tate Group over a Projective Base
نویسنده
چکیده
In this paper, we study deformations of pairs (C,G) where G is a (truncated) BarsottiTate group over a complete curve C on an algebraically closed field k of characteristic p. We prove that, if the curve C is a versal deformation of G, then there exists a unique lifting of the pair to the Witt ring W . We apply this result in the case of Shimura curves to obtain a lifting criterion. This result is also used in our work on how to define Shimura varieties in positive characteristics.
منابع مشابه
Deformation of a HW-Cyclic Barsotti-Tate Group
Let k be an algebrai ally losed eld of hara teristi p > 0, andG be a Barsotti-Tate over k. We denote by S the algebrai lo al moduli in hara teristi p of G, by G the universal deformation of G over S, and by U ⊂ S the ordinary lo us of G. The étale part of G over U gives rise to a monodromy representation ρG of the fundamental group of U on the Tate module of G. Motivated by a famous theorem of ...
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