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 …

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 prove the Ramanujan and Sato-Tate conjectures for Bianchi modular forms of weight at
least 2. More generally, we prove these conjectures for all regular algebraic cuspidal …

We associate infinitesimal characters to (twisted) families of $ L $-parameters and $ C $-
parameters of $ p $-adic reductive groups. We use the construction to study the action of the …

Let p be a prime number and K a finite extension of Q p. We state conjectures on the smooth
representations of GL n (K) that occur in spaces of mod p automorphic forms (for compact …

Let G be a split connected reductive algebraic group over Q p such that both G and its dual
group G ˆ have connected centers. Motivated by a hypothetical p-adic Langlands …

Suppose that G is a connected reductive group over a p-adic field F, that K is a hyperspecial
maximal compact subgroup of G (F), and that V is an irreducible representation of K over the …

We prove the weight elimination direction of the Serre weight conjectures as formulated by
Herzig for forms of U (n) which are compact at infinity and split at places dividing p in generic …

Let p be a prime number and f an overconvergent p-adic automorphic form on a definite
unitary group which is split at p. Assume that f is of “classical weight” and that its Galois …