The local Langlands correspondence for GL_n in families

Details The local Langlands correspondence for GL_n in families The local Langlands correspondence for GL_n in families

2011-04-02

arxiv.org/abs/1104.0321v1

Mathematics

Number Theory

61 papers

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The local Langlands correspondence for GL_n in families does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The local Langlands correspondence for GL_n in families, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The local Langlands correspondence for GL_n in families will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-335068