Let p be an odd prime and q a power of p. We examine the deformation theory of reducible and indecomposable Galois representations ρ̄ :Gℚ →GSp2n(𝔽q) that are unramified outside a finite set of primes S and whose image lies in a Borel subgroup. We show that under some additional hypotheses, such representations have geometric lifts to the Witt vectors W(𝔽q). The main theorem of this paper is a higher-dimensional generalization of the result of [S. Hamblen and R. Ramakrishna, Deformations of certain reducible Galois II, Amer. J. Math. 130(4) (2008) 913–944] [5].

中文翻译：

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某些可约伽罗瓦表示的变形 III

让p是一个奇数素数并且q一种力量p. 我们研究了可约和不可分解的伽罗瓦表示的变形理论ρ̄ ：Gℚ →GSP2n(𝔽q)在有限素数集之外没有分支的小号并且其图像位于 Borel 子群中。我们表明，在一些额外的假设下，这种表示对 Witt 向量有几何提升W(𝔽q). 本文的主要定理是 [S. Hamblen and R. Ramakrishna, Deformations of certain reducible Galois II,阿米尔。J.数学.130(4) (2008) 913–944] [5]。