Mazur's principle for U(2,1) Shimura varieties

Details Mazur's principle for U(2,1) Shimura varieties Mazur's principle for U(2,1) Shimura varieties

2006-06-28

arxiv.org/abs/math/0606731v1

Mathematics

Number Theory

20 pages; fullpage

Scientific paper

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".

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