Number Theory Seminar

I will discuss the 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. They are direct analogues of known explicit maps in the setting of modular curves and cyclotomic fields. I intend to motivate this through the lens of work-in-progress on "artificial complexes" that aims to provide explicit formulas in terms of Steinberg symbols of elliptic units, as in the cyclotomic setting.