We systematically classify strongly divisible φ-lattices, and present an explicit way to construct embedded Wach modules that correspond to crystalline representations with coefficients of the local absolute Galois group GQpa , where Qpa is the unramified extension of Qp of degree a. As applications we prove a theorem of Fontaine-Laffaille type on existence of integral Wach module when σ-invari...

For any number field F (not necessary of finite degree) and prime number p, let Lp(F ) denote the maximal unramified p-extension over F , and put G̃F (p) = Gal(Lp(F )/F ). Though the structure of G̃F (p) has been one of the most fascinating theme of number theory, our knowledge on it is not enough even at present: It had been a cerebrated open problem for a long time whether G̃F (p) can be infinit...

Preface. Imagery, language, and visuo-spatial thinking: E pluribus unum (Robert H. Logie & Michel Denis) Chapter 1. – The generation, maintenance, and transformation of visuo-spatial mental images (David Pearson, Rossana De Beni, & Cesare Cornoldi) Chapter 2. – Individual differences in visuo-spatial working memory (Tomaso Vecchi, Louise H. Phillips, & Cesare Cornoldi) Chapter 3. – Pictures in ...

We prove modularity lifting theorems for l-adic Galois representations of any dimension satisfying a unitary type condition and a Fontaine-Laffaille type condition at l. This extends the results of Clozel, Harris and Taylor ([CHT08]), and the subsequent work by Taylor ([Tay08]). The proof uses the Taylor-Wiles method, as improved by Diamond, Fujiwara, Kisin and Taylor, applied to Hecke algebras...

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Part I. Definitions of the operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. Definitions of N and F for curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1. The monodromy ope...

We say that a two dimensional p-adic Galois representation GF → GL2(Qp) of a number field F is weight two if it is de Rham with Hodge-Tate weights 0 and −1 equally distributed at each place above p; for example, the Tate module of an elliptic curve has this property. The purpose of this paper is to establish a variety of results concerning odd weight two representations of totally real fields i...

OBJECTIVES This article aims at describing, in a Belgian town, the frequency of the fear of falling and of subsequent activity restriction among non-institutionalised people aged 65 years and over, and at identifying persons affected by these two issues. METHODS Cross-sectional survey conducted in Fontaine l'Evêque (Belgium) in 2006, using a self-administered questionnaire. RESULTS The part...