  The complete exact solution of the Schwinger model with compact gauge group
U(1), in the Hamiltonian approach, is presented . The compactification is
imposed by demanding that the only surviving true electromagnetic degree of
freedom has angular character. Not surprinsingly, this topological condition
defines a version of the Schwinger model which is different from the standard
one, where $c$ takes values on the line . The main consequences are: the
spectra of the zero modes is not degenerated and does not correspond to the
equally spaced harmonic oscillator, both the electric charge and a modified
gauge invariant chiral charge are conserved (nevertheless, the axial-current
anomaly is still present) and, finally, there is no need to introduce a
$\theta$-vacuum. A comparison with the results of the standard Schwinger model
is pointed out along the text.
