  We explicitly calculate an arithmetic adelic quotient group for a locally
free sheaf on an arithmetic surface when the fiber over the infinite point of
the base is taken into account. The calculations are presented via a short
exact sequence. We relate the last term of this short exact sequence with the
projective limit of groups which are finite direct products of copies of
one-dimensional real torus and are connected with first cohomology groups of
locally free sheaves on the arithmetic surface.
