This paper is the first part of a work which proves Serre's modularity conjecture. We first
prove the cases p\not=2 and odd conductor, and p= 2 and weight 2, see Theorem 1.2 …

doi: 10.1093/imrn/rnp017 Page 1 Buzzard, K., and T. Gee. (2009) “Explicit Reduction
Modulo p of Certain Two-Dimensional Crystalline Representations,” International …

We classify the filtered modules with coefficients corresponding to two-dimensional
potentially semi-stable $ p $-adic representations of the Galois group of $\mathbf {Q} _p …

We show that the universal unitary completion of certain locally algebraic representation of
G:= GL 2 (ℚ p) with p> 2 is nonzero, topologically irreducible, admissible and corresponds to …

Let p be an odd prime number. Using the explicit description for irreducible GL2 (Qp)-
representations over Fp made in [Mo1], we determine all invariant elements of such …

MOD p GALOIS REPRESENTATIONS, (ϕ,Γ)-MODULES AND REPRESENTATIONS OF B2(Qp)
by Laurent Berger Page 1 MOD p GALOIS REPRESENTATIONS, (ϕ,Γ)-MODULES AND …

We show that the universal unitary completion of certain locally algebraic representation of
G:= GL 2 (ℚ p) with p> 2 is nonzero, topologically irreducible, admissible and corresponds to …