# Representation theory of reductive groups in characteristic $p$ as a limit of the theories in characteristic $0$

This question is out of plain curiosity. The first sentence of Deligne's Les corps locaux de caractéristique $p$, limites de corps locaux de caractéristique $0$ (1984) reads (in rough translation) as follows :

D. Kazhdan has introduced the principle that the representation theory of a reductive group over a local field of prime characteristic $p$ is the limit, as the ramification index tends to infinity, of theories over local fields of characteristic $0$ with the same residue field.

He says that according to Langlands' philosophy, one should expect the same phenomenon to occur on the galoisian side, and goes on to establish a precise equivalence of categories justifying this principle (and clarifying the earlier work of M. Krasner from the forties).

I'm mainly interested in this side of the story, but I'm curious as to where Kazhdan's principle in representation theory was first enunciated. What are the standard references in English or French explaining this principle ?

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This may be hard to pin down in the published literature, so I'd suggest asking Kazhdan directly. It's helpful anyway to add MathSciNet data for Deligne's paper, where the reviewer E. Zink states that Kazhdan's principle was "recently introduced": MR771673 (86g:11068) Deligne, P. Les corps locaux de caracte ́ristique p, limites de corps locaux de caracte ́ristique 0. (French) [Local fields of characteristic p which are limits of local fields of characteristic 0], Representations of reductive groups over a local field, 119–157, Travaux en Cours, Hermann, Paris, 1984. –  Jim Humphreys Feb 21 '12 at 14:33