Automorphic forms and rational homology 3-spheres.
We show that it is possible in rather general situations to obtain a finite-dimensional modular representation of the Galois group of a number field as a constituent of one of the modular Galois representations attached to automorphic representations of a general linear group over , provided one works “potentially.” The proof is based on a close study of the monodromy of the Dwork family of Calabi–Yau hypersurfaces; this in turn makes use of properties of rigid local systems and the classification...
Nous donnons une preuve que tout automorphisme sauvagement ramifié d’un corps de séries formelles à une variable et à coefficients dans un corps parfait de caractéristique provient de la construction du corps des normes d’une -extension totalement ramifiée d’un corps local de caractéristique ou .
We construct an uncountable set of strong automorphisms of the Witt ring of a global field.