## From local class field theory to the curve and vice versa

Laurent Fargues

Institut de mathématiques de Jussieu

October 29, 2015

I will speak about results contained in my article "$G$-torseurs en théorie de Hodge $p$-adique" linked to local class field theory. I will in particular explain the computation of the Brauer group of the curve and why its fundamental class is the one from local class field theory.