Mod p Hecke algebras and dual equivariant cohomology I: the case of $GL_2$

Cédric Pépin (1) , Tobias Schmidt (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 LESIA (UMR_8109) - Laboratoire d'études spatiales et d'instrumentation en astrophysique

Let $F$ be a p-adic local field and $G=GL_2(F)$. Let $\mathcal{H}^{(1)}$ be the pro-p Iwahori-Hecke algebra of $G$ with coefficients in an algebraic closure of $\mathbb{F}_p$. We show that the supersingular irreducible $\mathcal{H}^{(1)}$-modules of dimension 2 can be realized through the equivariant cohomology of the flag variety of the mod p Langlands dual group of $G$.

Domaines: Théorie des nombres [math.NT]

Cédric Pépin, Tobias Schmidt. Mod p Hecke algebras and dual equivariant cohomology I: the case of $GL_2$. 2019. ⟨hal-02338672⟩