The local Langlands correspondence for GL_n in families
By M. Emerton, David Helm. 2011
79 citations recorded by the source corpus.
Let E be a nonarchimedean local field with residue characteristic l, and suppose we have an n-dimensional representation of the absolute Galois group G_E of E over a reduced complete Noetherian local ring A with finite residue field k of characteristic p different from l. We consider the problem of associating to any such representation an admissible A[GL_n(E)]-module in a manner compatible with the local Langlands correspondence at characteristic zero points of Spec A. In particular we give a set of conditions that uniquely characterise such an A[GL_n(E)]-module if it exists, and show that such an A[GL_n(E)]-module always exists when A is the ring of integers of a finite extension of Q_p. We also use these results to define a "modified mod p local Langlands correspondence" that is more compatible with specialization of Galois representations than the mod p local Langlands correspondence of Vigneras.
View Paper: https://www.semanticscholar.org/paper/1e3ae4f80d043ac0b890ec2ab42ec4eb1706c0f7
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- Frank Calegari
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- Thomas Barnet-Lamb
- J. Thorne
- M. Emerton
Citations in the corpus
- Modularity lifting beyond the Taylor–Wiles method (2012, background): “13 of [EH11], it follows that π′ has the same supercuspidal support as π.”