  Let T be a split torus over local or global function field. The theory of
Brylinski-Deligne gives rise to the metaplectic central extensions of T by a
finite cyclic group. The representation theory of these metaplectic tori has
been developped to some extent in the works of M. Weissman, G. Savin, W. T.
Gan, P. McNamara and others. In this paper we propose a geometrization of this
theory in the framework of the geometric Langlands program (in the everywhere
nonramified case).
