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The term Galois representation is frequently used when the G-module is a vector space over a field or a free module over a ring, but can also be used as a synonym for G-module. The study of Galois modules for extensions of local or global fields is an important tool in number theory.
7
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Semisimple Weil-Deligne representations
I've just realized that I don't understand something important and basic about the Weil-Deligne group and its representations. (I'm not very surprised by this).
Following Deligne's article, Section …
12
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What are the local Langlands conjectures nowadays, for connected reductive groups over a $p$...
First, I'd like to second the reference given by JT: David Vogan, "The local Langlands conjecture", appearing in Representation Theory of Groups and Algebras (J. Adams et al., eds. Contemporary Mathe …