Sur quelques propriétés des algèbres de Hecke quaternioniques

Terracini, Lea

Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 3, pp. 677-700

Résumé

Let $B$ be an indefinite quaternion algebra over $\mathbf{Q}$, of discriminant divisible by a prime $p$. We introduce the space of quaternionic automorphic forms of level $p^{s}$ and the algebra of Heche operators acting on it. By making use of the Jacquet-Langlands correspondence we show that this algebra is a quotient of a classical Hecke algebra (without the $T_{p}$ operator). We deduce that the quaternionic Hecke algebra is free of finite rank over $\mathbf{Z}$ and that it is compatible with base change.