Appropriate Citations

Once I wrote a paper (two, in fact) on even Galois representations. The second paper in particular proved what I thought was a fairly definitive result ruling out the existence of a wide class of even de Rham representations with distinct Hodge-Tate weights. It turns out that almost nobody seems to cite these results, probably because they aren’t particularly useful — at least in any obvious sense. On the other hand, almost everyone who does cite the paper seems to cite it for a specific proposition (3.2) which is an easy consequence of the results of Moret-Bailly. The proposition, more or less, is a potential inverse Galois problem with (any finite collection) of local conditions. The main application of such a proposition (both in my paper and in papers which cite it) is that, given a local mod-\(p\) representation which looks like it could come (say) from the localization of a global representation associated to an automorphic form, the proposition often allows one to produce such a form at the cost of making a finite totally real extension in which \(p\) splits completely. This suffices for many purposes.

It turns out, however, that the lemma (pretty much in an equivalent form by an equivalent argument) was already proved by Moret-Bailly himself in this paper. This means that if you cite my paper for this particular lemma, you should definitely cite the paper of Moret-Bailly. Of course, if you are also applying it in a context similar to my paper (say in order to construct automorphic forms with certain local properties), you should certainly feel free to continue to cite my paper as well.

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