  We compute the noncommutative de Rham cohomology for the finite-dimensional
q-deformed coordinate ring $C_q[SL_2]$ at odd roots of unity and with its
standard 4-dimensional differential structure. We find that $H^1$ and $H^3$
have three additional modes beyond the generic $q$-case where they are
1-dimensional, while $H^2$ has six additional modes. We solve the spin-0 and
Maxwell theory on $C_q[SL_2]$ including a complete picture of the self-dual and
anti-self dual solutions and of Lorentz and temporal gauge fixing. The system
behaves in fact like a noncompact space with self-propagating modes (i.e., in
the absence of sources). We also solve with examples of `electric' and
`magnetic' sources including the biinvariant element $\theta\in H^1$ which we
find can be viewed as a source in the local (Minkowski) time-direction (i.e. a
uniform electric charge density).
