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I'd like a detailed proof in English of Laumon's proof that the two Fourier-Mukai transforms taking the derived category of quasicoherent sheaves on $\mathbb{G}_m$-local systems of a curve $X$ to the derived category of $D$-modules on $Bun_{\mathbb{G}_m}(X)$ are mutually inverse.

Laumon's original (unpublished) paper, Transformation de Fourier généralisée is on the arXiv: alg-geom/9603004, but I'd ideally like an English translation, or at least an expository paper in English.

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  • $\begingroup$ Easy to find, but even easier when one is provided a title or other reference. $\endgroup$
    – David Roberts ♦
    Commented Feb 25, 2019 at 1:02
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    $\begingroup$ @DavidRoberts Edited $\endgroup$
    – Exit path
    Commented Feb 25, 2019 at 1:20

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I would be surprised if there is a translation of Laumon. However, you can look the beginning section of Schnell's Holonomic D-modules on abelian varieties for a summary of some of Laumon's results.

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