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 L-value of a Hecke character providing evidence for a conjecture of Harder that the denominator is given by this L-value. We also prove under some additional assumptions that the restriction of the classes to the boundary of the Borel-Serre compactification of the spaces is integral. Such classes are interesting for their use in congruences with cuspidal classes to prove connections between the special L-value and the size of the Selmer group of the Hecke character.
Keywords
Cite
@article{arxiv.math/0606531,
title = {Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields},
author = {Tobias Berger},
journal= {arXiv preprint arXiv:math/0606531},
year = {2010}
}
Comments
37 pages; strengthened integrality result (Proposition 16), corrected statement of Theorem 3, and revised introduction