The construction of the p-adic local Langlands correspondence for \mathrm{GL}_2(\mathbf{Q}_p) uses in an essential way Fontaine's theory of cyclotomic (\varphi

Understanding Galois representations is one of the central goals of number theory. Around 1990, Fontaine devised a strategy to compare such p-adic Galois repres

The construction of the p-adic local Langlands correspondence for GL2(Qp) uses in an essential way Fontaine's theory of cyclotomic (φ,Γ)-modules. Here cycloto

This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a pri

Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to