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Abstract:
Continuous representations of p-adic Lie groups with p-adic
coeffients arise naturally in a variety of situations in number
theory. Attempts to develop a systematic theory of such
representations have been hampered by the impossibility of
defining Haar measure with p-adic values. Nevertheless,
there has been tremendous progress in recent years: Schneider
and Teitelbaum have defined a category of p-adic
representations to which differential techniques can be
applied, Emerton has applied their work to p-adic
modular forms, and Breuil has provided evidence for
a p-adic local Langlands correspondence. The goal
of this talk is to justify the speaker's conviction that
this is the branch of representation theory that will see
the most striking developments over the next decade.
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