Barsotti-Tate的潜在变形计算
Un calcul d'anneaux de déformations potentiellement Barsotti--Tate
摘要：
设F是Qp的一个非分歧扩张.本文的第一个目的是发展一个纯局部方法来计算F的绝对伽罗瓦群的具有驯服伽罗瓦型不可约二维表示的潜在Barsotti-Tate变形环。然后，我们应用我们的方法在特定的情况下，F有2度在Q_p和确定这种方式几乎所有的这些变形环。在这种特殊情况下，我们观察到这些变形环的结构和相关的Kisin品种的几何形状之间的密切关系。作为推论，并仍然假设F在Q_p上的度为2，我们证明了Kisin的一个猜想，除了两个非常特殊的情况，该猜想预言了内禀伽罗瓦重数都等于0或1。
英文摘要：
Let F be an unramified extension of Qp. The first aim of this work is to develop a purely local method to compute the potentially Barsotti-Tate deformations rings with tame Galois type of irreducible two-dimensional representations of the absolute Galois group of F. We then apply our method in the particular case where F has degree 2 over Q_p and determine this way almost all these deformations rings. In this particular case, we observe a close relationship between the structure of these deformations rings and the geometry of the associated Kisin variety. As a corollary and still assuming that F has degree 2 over Q_p, we prove, except in two very particular cases, a conjecture of Kisin which predicts that intrinsic Galois multiplicities are all equal to 0 or 1.
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