Pro-p-Iwahori invariants for SL_2 and L-packets of Hecke modules
Abstract
Let p be a prime number, and F a nonarchimedean local field of residual characteristic p. We explore the interaction between the pro-p-Iwahori-Hecke algebras of the group GL_n(F) and its derived subgroup SL_n(F). Using the interplay between these two algebras, we deduce two main results. The first is an equivalence of categories between Hecke modules in characteristic p over the pro-p-Iwahori-Hecke algebra of SL_2(Q_p) and smooth mod-p representations of SL_2(Q_p) generated by their pro-p-Iwahori-invariants. The second is a "numerical correspondence" between packets of supersingular Hecke modules in characteristic p over the pro-p-Iwahori-Hecke algebra of SL_n(F), and irreducible, n-dimensional projective Galois representations.
Keywords
Cite
@article{arxiv.1308.6239,
title = {Pro-p-Iwahori invariants for SL_2 and L-packets of Hecke modules},
author = {Karol Koziol},
journal= {arXiv preprint arXiv:1308.6239},
year = {2015}
}
Comments
24 pages. Previously titled "Restriction of pro-p-Iwahori-Hecke modules." Simply-connected assumption removed, other results unchanged. To appear in IMRN