# Eisenstein cocycles for imaginary quadratic fields

# Eisenstein cocycles for imaginary quadratic fields

**Note the new time and location**

I will describe a construction of maps from the homology of Bianchi spaces for an imaginary quadratic field F to second K-groups of ray class fields of F. These maps are “Eisenstein” in the sense that they factor through the quotient by the action of an Eisenstein ideal way from the level. These long-expected maps are direct analogues of known, explicit Eisenstein maps the setting of modular curves and cyclotomic fields. We use and refine a method Venkatesh and I developed in order to construct Eisenstein GL_2-cocycles valued in the second K-groups of function fields of products of two CM elliptic curves. The desired maps arise from pulling back restrictions of these cocycles at torsion points. I will explain some of the key steps in and obstructions to carrying this out. This is joint work with E. Lecouturier, S. Shih, and J. Wang.

**Meeting ID: 920 2195 5230**

**Passcode: The three-digit integer that is the cube of the sum of its digits.**