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Aspects of the mod p representation theory of p-adic reductive groups

Introductory Workshop: New Geometric Methods in Number Theory and Automorphic Forms August 18, 2014 - August 22, 2014

August 20, 2014 (11:30 AM PDT - 12:30 PM PDT)
Speaker(s): Rachel Ollivier (University of British Columbia)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC


These lectures will focus on the mod p representation theory of a split p-adic reductive group G, using  GL(2) as a running example. We hope to emphasize the differences between the mod p and complex representations of G while keeping in mind that the theory is partly motivated by the mod p and complex local Langlands programs.


We will start with remarks regarding finite reductive groups. We will then compare the homological properties of certain categories of mod p and complex representations of G (and the associated pro-p-Iwahori Hecke algebra). In particular, in the complex setting, the theory of coefficient systems on the Bruhat-Tits building by Schneider and Stuhler gives a way to construct explicit projective resolutions. We will explore what remains from this theory in the mod p setting. This will help us describe the first step in the construction of Colmez' functor yielding the mod p local Langlands correspondence for GL(2,Q_p).

21415?type=thumb Olivier Notes 878 KB application/pdf Download
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H.264 Video 14056.mp4 330 MB video/mp4 rtsp://videos.msri.org/data/000/021/364/original/14056.mp4 Download
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