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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For any reductive group $ G $ over a global function field, we use the cohomology of $ G $-
shtukas with multiple modifications and the geometric Satake equivalence to prove the …

We prove the finiteness and compatibility with base change of the $(\varphi,\Gamma) $-
cohomology and the Iwasawa cohomology of arithmetic families of $(\varphi,\Gamma) …

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 …

We prove a conjecture of Colmez concerning the reduction modulo p of invariant lattices in
irreducible admissible unitary p-adic Banach space representations of GL2 (Q p) with p≥ 5 …

Let F be a CM number field. We prove modularity lifting theorems for regular n-dimensional
Galois representations over F without any self-duality condition. We deduce that all elliptic …

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 …

Let F be a totally real field, K/F a totally imaginary quadratic extension, d=[F: Q], c∈ Gal (K/F)
the non-trivial Galois automorphism. Let n be a positive integer and G= Gn be the algebraic …

Let1 G be a profinite group which is topologically finitely generated, 2 pa prime number and
d≥ 1 an integer. We show that the functor from rigid analytic spaces over Qp to sets, which …