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Number Theory Seminar

Thursday, April 5, 2018
4:00pm to 5:00pm
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Building 15, Room 104
Some calculations with higher pro-p-Iwahori cohomology
Karol Koziol, Department of Mathematics, University of Toronto,
Let G denote a p-adic reductive group, and I_1 a pro-p-Iwahori subgroup. A classical result of Borel and Bernstein shows that the category of complex G-representations generated by their I_1-invariant vectors is equivalent to the category of modules over the (pro-p-)Iwahori-Hecke algebra H. This makes the algebra H an extremely useful tool in the study of complex representations of G, and thus in the Local Langlands Program. When the field of complex numbers is replaced by a field of characteristic p, the equivalence above no longer holds. However, Schneider has shown that one can recover an equivalence if one passes to derived categories, and upgrades H to a certain differential graded Hecke algebra. We will attempt to understand this equivalence by examining the H-module structure of certain higher I_1-cohomology spaces, with coefficients in mod-p representations of G. If time permits, we'll discuss how these results are compatible with Serre weight conjectures of Herzig and Gee--Herzig--Savitt.
For more information, please contact Mathematics Dept. by phone at 626-395-4335 or by email at mathinfo@caltech.edu.