Denominators of Eisenstein cohomology classes for \(\text{GL}_2\) over imaginary quadratic fields
G. Harder initiated a program to describe the cohomology of arithmetic groups in terms of cusp forms and Eisenstein series. Following this program, the author studies the arithmetic of Eisenstein cohomology classes for symmetric spaces associated to \(\text{GL}_2\) over imaginary quadratic fields. In particular, he proves a lower bound for the denominator of degree \(1\) Eisenstein classes in terms of a special \(L\)-value of a Hecke character, as conjectured by Harder. He also provides conditions under which the restriction of the Eisenstein classes to the boundary of the Borel-Serre compactification of the symmetric space is integral.
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