Parabolic induction and Hecke modules in characteristic p for p-adic GLn

We classify the simple supersingular modules for the pro-p-Iwahori Hecke algebra H of p-adic GL(n) by proving a conjecture by Vigneras about a mod p numerical Langlands correspondence on the side of the Hecke modules. We define a process of induction for H-modules in characteristic p that reflects the parabolic induction for representations of the p-adic general linear group and explore the semisimplification of the standard nonsupersingular H-modules in light of this process.