We consider stacks of filtered φ-modules over rigid analytic spaces and adic spaces. We show that these modules parametrize p-adic Galois representations of the absolute Galois group of a p-adic field with varying coefficients over an open substack containing all classical points. Further we study a period morphism (defined by Pappas and Rapoport) from a stack parametrising integral data and de...

Suppose F = W (k)[1/p] where W (k) is the ring of Witt vectors with coefficients in algebraically closed field k of characteristic p 6= 2. We construct integral theory of p-adic semi-stable representations of the absolute Galois group of F with Hodge-Tate weights from [0, p). This modification of Breuil’s theory results in the following application in the spirit of the Shafarevich Conjecture. I...

Let g = ∑ c(D) qD and f = ∑ an q n be modular forms of half-integral weight k + 1/2 and integral weight 2k respectively which are associated to each other under the ShimuraKohnen correspondence. For suitable fundamental discriminants D, a theorem of Waldspurger relates the coe cient c(D) to the central critical value L(f,D, k) of the Hecke L-series of f twisted by the quadratic Dirichlet charac...

1. In this note we announce a vanishing theorem for the cohomology of discrete subgroups of p-adic groups. The methods and results bear a striking analogy with the real case (see Matsushima [4]). In particular, we define "p-adic curvature" for the p-adic symmetric spaces of Bruhat-Tits (see [1]). As in the real case, we then reduce the proof of our vanishing theorem to the assertion that the mi...

We prove potential automorphy results for a single Galois representation $$G_F\rightarrow GL_n(\overline{\mathbb {Q}}_l)$$ where F is CM number field. The strategy to use the p, q switch trick go between p-adic and q-adic realisation of certain variant Dwork motive. choose this break self-duality shape motives, but not Hodge-Tate weights. Another key result that representations we come from mot...

and Applied Analysis 3 By 2.2 , we get μf,−q ( a pZp ) 2 q 2 qp −qa ∫ Zp f ( a px ) dμ−qpn x . 2.3 Therefore, by 2.3 , we obtain the following theorem. Theorem 2.1. For f, g ∈ C Zp , one has μαf βg,−q αμf,−q βμg,−q, 2.4 where α, β are constants. From 2.2 and 2.4 , we note that ∣μf,−q ( a pZp )∣∣ ≤ M‖f‖∞, 2.5 where ‖f‖∞ supx∈Zp |f x | and M is some positive constant. Now, we recall the definitio...