Seminars: Lebacque Philippe, On the Cohomological Dimension of Some Pro-p-Extensions

SEMINARS


The joint seminar of the Sector 4.1 (IITP RAS) and Poncelet French-Russian laboratory "Arithmetic Geometry and Coding Theory" March 20, 2013 17:30, Moscow, IUM (Bolshoi Vlas'evskii per., 11), room 304

On the Cohomological Dimension of Some Pro-p-Extensions Lebacque Philippe^ab ^a Laboratoire J.-V. Poncelet, Independent University of Moscow ^b Laboratoire de Mathématiques, Université de Franche-Comté, Besançon
Abstract: This talk deals with pro-p-extensions of number fields and function fields with cohomological dimension at most 2. I will first recall some old results concerning Galois groups of type $G_S( p)$, then I will discuss the method introduced by Labute and Schmidt to control the case "S finite" and give some corollaries concerning Tsfasman-Vladuts $\phi_q$'s, and I will conclude giving new situations for number fields with $cd_pG=<2$ (joint work with Blondeau and Maire).