Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Jacobians and explicit descents   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.

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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg