Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields
Abstract
We study the arithmetic of Eisenstein cohomology classes (in the sense of G. Harder) for symmetric spaces associated to GL_2 over imaginary quadratic fields. We prove in many cases a lower bound on their denominator in terms of a special Lvalue of a Hecke character providing evidence for a conjecture of Harder that the denominator is given by this Lvalue. We also prove under some additional assumptions that the restriction of the classes to the boundary of the BorelSerre compactification of the spaces is integral. Such classes are interesting for their use in congruences with cuspidal classes to prove connections between the special Lvalue and the size of the Selmer group of the Hecke character.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606531
 Bibcode:
 2006math......6531B
 Keywords:

 Mathematics  Number Theory;
 11F75;
 11F67;
 22E41
 EPrint:
 37 pages