Sur quelques propriétés des algèbres de Hecke quaternioniques

Let B be an indefinite quaternion algebra over 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 JacquetLanglands 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 Z and that it is compatible with base change.