Series: Annals of Mathematics Studies

A foundational account of a new construction in the p-adic Langlands correspondence Motivated by the p-adic Langlands program, Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts constructs stacks that algebraize Mazur's formal deformation rings of local Galois representations. More precisely, it constructs Noetherian formal algebraic stacks over Spf Zp that parameterise étale (ϕ, Γ)-modules. The formal...

A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations...