Let ff be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric
power lifting Sym nf Sym^nf for every n≥ 1 n≧1. We establish the same result for a more …

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math f</jats: tex-math>< mml: math xmlns: mml=" http://www. w3. org/1998/Math/MathML"> …

We prove an automorphy lifting theorem for l-adic representations where we impose a new
condition at l, which we call" potentential diagonalizability." This result allows for" change of …

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 …

In 1987 Serre conjectured that any mod ℓ 2-dimensional irreducible odd representation of
the absolute Galois group of the rationals came from a modular form in a precise way. We …

Elliptic curves over real quadratic fields are modular | SpringerLink Skip to main content
Advertisement SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home …

We prove new automorphy lifting theorems for essentially conjugate self-dual Galois
representations into GLn. Existing theorems require that the residual representation have …

We prove the Breuil–Mézard conjecture for two-dimensional potentially Barsotti–Tate
representations of the absolute Galois group (up to the question of determining precise …

A GEOMETRIC PERSPECTIVE ON THE BREUIL–MÉZARD CONJECTURE Page 1 J. Inst. Math.
Jussieu (2014) 13(1), 183–223 183 doi:10.1017/S147474801300011X c Cambridge University …

We formulate a conjecture generalising the weight in Serre's Conjecture to n-dimensional
representations ρ: Gal ([special characters omitted])→ GL n ([special characters omitted]) …