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 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 …

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 …

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 …

On the asymptotic Fermat’s last theorem over number fields Page 1 Comment. Math. Helv. 93
(2018), 359–375 DOI 10.4171/CMH/437 Commentarii Mathematici Helvetici © Swiss …

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 …