Sur quelques propriétés des algèbres de Hecke quaternioniques
Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 3, pp. 677-700
Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica
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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.
Terracini, Lea. Sur quelques propriétés des algèbres de Hecke quaternioniques. Bollettino della Unione matematica italiana, Série 8, 5B (2002) no. 3, pp. 677-700. http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_3_a6/
@article{BUMI_2002_8_5B_3_a6,
author = {Terracini, Lea},
title = {Sur quelques propri\'et\'es des alg\`ebres de {Hecke} quaternioniques},
journal = {Bollettino della Unione matematica italiana},
pages = {677--700},
year = {2002},
volume = {Ser. 8, 5B},
number = {3},
zbl = {1177.11046},
mrnumber = {MR1934374},
url = {http://geodesic.mathdoc.fr/item/BUMI_2002_8_5B_3_a6/}
}