Mazur's principle for U(2,1) Shimura varieties
Abstract
Mazur's principle gives a criterion under which an irreducible mod l Galois representation arising from a classical modular form of level Np (with p prime to N) also arises from a classical modular form of level N. We consider the analogous question for Galois representations arising from certain unitary Shimura varieties. In particular, we prove an analoge of Mazur's principle for U(2,1) Shimura varities. We also give a conjectural criterion for a Galois representation arising in the cohomology of a unitary Shimura variety whose level subgroup is parahoric at p to also arise in the cohomology of a Shimura variety with "less level structure at p".
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606731
 Bibcode:
 2006math......6731H
 Keywords:

 Mathematics  Number Theory;
 11F80;
 11F33;
 11G18
 EPrint:
 20 pages