On an analogue of a conjecture of Sharifi for imaginary quadratic fields

Abstract: We explore a relation between the cohomology of certain Bianchi 3-folds, modulo some Eisenstein ideal, to the arithmetic of imaginary quadratic fields. For instance, in the case of Euclidean imaginary quadratic fields, we get a relation between modular symbols and cup-products of elliptic units. This is similar to conjectures of Sharifi for classical modular curves, relating modular symbols to cup-product of cyclotomic units. This is work in progress with Jun Wang.

number theory

Audience: researchers in the topic

London number theory seminar

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