Abstract
We show that the irregular connection on \({\mathbb {G}}_m\) constructed by Frenkel and Gross (Ann Math 170–173:1469–1512, 2009) and the one constructed by Heinloth et al. (Ann Math 177–181:241–310, 2013) are the same, which confirms Conjecture 2.16 of Heinloth et al. (Ann Math 177–181:241–310, 2013).
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Notes
Note that it is not a sheaf.
Recall that given a line bundle \({\mathcal {L}}\) on an algebraic variety X, it makes sense to talk about \({\mathcal {L}}^{\lambda }\)-twisted D-modules on X for any \({\lambda }\in {\mathbb {C}}\).
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Acknowledgments
The author thanks the referee for careful reading and critical questioning of the early version of the note. The author also thanks T.-H. Chen and M. Kamgarpour for very useful comments. The work is partially supported by NSF Grant DMS-1001280/1313894 and DMS-1303296/1535464 and the AMS Centennial Fellowship.
