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 …

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

We study G-valued Galois deformation rings with prescribed properties, where G is an
arbitrary (not necessarily connected) reductive group over an extension of ℤ l for some …

A foundational account of a new construction in the p-adic Langlands correspondence
Motivated by the p-adic Langlands program, this book constructs stacks that algebraize …

Caraiani was supported in part by NSF grant DMS-1501064, by a Royal Society University
Research Fellowship, and by ERC Starting Grant 804176. Emerton was supported in part by …

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 …

We prove the weight part of Serre's conjecture in generic situations for forms of U (3) which
are compact at infinity and split at places dividing p as conjectured by Herzig (Duke Math J …

Let K/Q p be unramified. Inside the Emerton–Gee stack X 2, one can consider the locus of
two-dimensional mod 𝑝 representations of Gal⁢(K ̄/K) having a crystalline lift with specified …

We prove a local–global compatibility result in the mod $ p $ Langlands program for
$\mathrm {GL} _2 (\mathbf {Q} _ {p^ f}) $. Namely, given a global residual representation …