Cohomological Weight Shiftings for Automorphic Forms on Definite Quaternion Algebras

Details Cohomological Weight Shiftings for Automorphic Forms on Definite Quaternion Algebras Cohomological Weight Shiftings for Automorphic Forms on Definite Quaternion Algebras

2011-10-31

arxiv.org/abs/1110.6871v1

Mathematics

Number Theory

43 pages. Comments are very welcome

Scientific paper

Let F/Q be a totally real field extension of degree g and let D be a definite quaternion algebra with center F. Fix an odd prime p which is unramified in F and D. We produce weight shiftings between (mod p) automorphic forms on the multiplicative group of D having fixed level. When the starting weight does not contain any (2,...,2)-block, we obtain these shiftings via maps induced in cohomology by intertwining operators acting on F_{p}-representations of GL(2,O_{F}/pO_{F}). Shiftings by (p-1,...,p-1) for weights containing (2,...,2)-blocks are obtained following the methods of Edixhoven-Khare, as half of our intertwining operators becomes trivial in this case.

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