Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts

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 Mazur’s formal deformation rings of local Galois representations. More precisely, it constructs Noetherian formal algebraic stacks over Spf Z p that parameterize étale (ϕ, Γ)-modules; the formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representation