GALOIS REDUCIBILITY AND FREENESS OF THE COHOMOLOGY OF KHT SHIMURA VARIETIES

Pascal Boyer (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

In a previous paper, we proved that the $\overline{\mathbb Z}_l$-cohomology of KHT Shimura varieties of dimension $d$ which is not prime, whatever is the weight of the coefficients, when the level is large enough at $l$, always contains non trivial torsion classes. For other compact PEL Shimura varieties and for a generic maximal ideal $\mathfrak m$ of the unramified Hecke algebra, the localisation at $\mathfrak m$ of these cohomology groups is known to be free. In this work we obtain the same result for $\mathfrak m$ such that its associated galoisian $\overline{\mathbb F}_l$-representation $\overline \rho_{\mathfrak m}$ is irreducible.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Pascal Boyer. GALOIS REDUCIBILITY AND FREENESS OF THE COHOMOLOGY OF KHT SHIMURA VARIETIES. 2019. ⟨hal-02080476v3⟩