Eisenstein cocycles for imaginary quadratic fields
Romyar Sharifi (University of California, Los Angeles)
Abstract: 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. This is largely joint work with E. Lecouturier, S. Shih, and J. Wang, though 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.
number theory
Audience: researchers in the discipline
( paper )
| Organizers: | Sol Friedberg*, Benjamin Howard, Dubi Kelmer, Spencer Leslie, Keerthi Madapusi Pera, Bjorn Poonen*, Andrew Sutherland*, Wei Zhang* |
| *contact for this listing |