Arithmetic properties of Eisenstein series for $GL_n$ over imaginary quadratic fields

Virtual talk.

I will discuss the arithmetic of certain degree $N-1$ Eisenstein cohomology classes for $GL_n$ over an imaginary quadratic field $k$. Under natural conditions one can evaluate these classes explicitly on the $(N-1)$-cycles associated to degree $N$ extensions of $k$. As a consequence I will discuss the proof of a remarkable conjecture of Sczech and Colmez expressing certain critical values of $L$-functions of Hecke characters in terms of simple polynomials in Kronecker-Eisenstein series.