Aspects of the mod p representation theory of padic reductive groups
Introductory Workshop: New Geometric Methods in Number Theory and Automorphic Forms August 18, 2014  August 22, 2014
Location: SLMath: Eisenbud Auditorium
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These lectures will focus on the mod p representation theory of a split padic 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 propIwahori Hecke algebra). In particular, in the complex setting, the theory of coefficient systems on the BruhatTits 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).
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