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"> …

Patching and the p-adic local Langlands correspondenceT1 Page 1 arXiv:1310.0831v5 [math.NT]
1 Jul 2016 Cambridge Journal of Mathematics Volume 0, Number 0, 1, 2014 Patching and the …

arXiv:2210.01404v2 [math.NT] 1 Feb 2023 Page 1 An introduction to the categorical p-adic
Langlands program Matthew Emerton, Toby Gee, and Eugen Hellmann Abstract. We give an …

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 number of related generalisations of the weight part of Serre's conjecture to
the case of GLn over an arbitrary number field, motivated by the formalism of the Breuil …

We construct projective varieties in mixed characteristic whose singularities model, in
generic cases, those of tamely potentially crystalline Galois deformation rings for unramified …

COMPOSITIO MATHEMATICA Page 1 COMPOSITIO MATHEMATICA Compositio Math. doi:10.1112/S0010437X13007653
FOUNDATION COMPOSITIO MATHEMATICA 150 (2014), Level-raising and symmetric …

Let p be a prime number, F a totally real number field unramified at places above p and D a
quaternion algebra of center F split at places above p and at no more than one infinite place …

We construct stacks which algebraize Mazur's formal deformation rings of local Galois
representations. More precisely, we construct Noetherian formal algebraic stacks over Spf …