  We develop a cohomological description of various explicit descents in terms
of generalized Jacobians, generalizing the known description for hyperelliptic
curves. Specifically, given an integer $n$ dividing the degree of some reduced
effective divisor $\mathfrak{m}$ on a curve $C$, we show that multiplication by
$n$ on the generalized Jacobian $J_\frak{m}$ factors through an isogeny
$\varphi:A_{\mathfrak{m}} \rightarrow J_{\mathfrak{m}}$ whose kernel is
naturally the dual of the Galois module
$(\operatorname{Pic}(C_{\overline{k}})/\mathfrak{m})[n]$. By geometric class
field theory, this corresponds to an abelian covering of $C_{\overline{k}} := C
\times_{\operatorname{Spec}{k}} \operatorname{Spec}(\overline{k})$ of exponent
$n$ unramified outside $\mathfrak{m}$. The $n$-coverings of $C$ parameterized
by explicit descents are the maximal unramified subcoverings of the $k$-forms
of this ramified covering. We present applications of this to the computation
of Mordell-Weil groups of Jacobians.
