Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields

Details Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields

2006-06-21

arxiv.org/abs/math/0606531v2

Manuscripta Math. 125 (2008), no. 4, 427--470

Mathematics

Number Theory

37 pages; strengthened integrality result (Proposition 16), corrected statement of Theorem 3, and revised introduction

Scientific paper

10.1007/s00229-007-0139-6

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.

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