On the Cohomological Dimension of Some Pro-p-Extensions (О когомологической размерности некоторых про-p-расширений)

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).