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 …

Serre’s modularity conjecture (II) Page 1 Invent math (2009) 178: 505–586 DOI 10.1007/s00222-009-0206-6
Serre’s modularity conjecture (II) Chandrashekhar Khare · Jean-Pierre Wintenberger …

We prove new cases of the Fontaine-Mazur conjecture, that a $2 $-dimensional $ p $-adic
representation $\rho $ of $ G_ {\mathbb {Q}, S} $ which is potentially semi-stable at $ p …

We prove the existence in many cases of minimally ramified p-adic lifts of 2-dimensional
continuous, odd, absolutely irreducible, mod p representations p̄ of the absolute Galois …

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 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 …

We prove the existence in many cases of minimally ramified $ p $-adic lifts of 2-dimensional
continuous, odd, absolutely irreducible, mod $ p $ representations $\overline {\rho} $ of the …

We give an algorithm for computing the reduction modulo p of 2-dimensional crystalline
representations of Gal (Qp/Qp). This algorithm relies on Fontaine's theory of (ϕ, Γ)-modules …

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 …

A. Wiles udowodnił w pracy [72], że w przypadku semistabilnej krzywej eliptycznej E
określonej nad Q, nieprzywiedlność i modularność reprezentacji ρE, p dla pewnej …