Eisenstein cocycles for imaginary quadratic fields

2025/04/27 by Lecouturier, Emmanuel, Sharifi, Romyar, Shih, Sheng-Chi +1 · 1 citation
#11F75 #11G05 #11G15 #11R70 #19E15 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.19125

Abstract

We construct Eisenstein cocycles for arithmetic subgroups of GL₂ of imaginary quadratic fields valued in second K-groups of products of two CM elliptic curves. We use these to construct maps from the first homology groups of Bianchi spaces to corresponding second K-groups of ray class fields and to verify the Eisenstein property of these maps for prime-to-level Hecke operators.

Citations

• Level compatibility in Sharifi's conjecture
• Eisenstein cohomology classes for GL_N over imaginary quadratic fields
• Eisenstein-Kronecker classes, integrality of critical values of Hecke L-functions and p-adic interpolation
• Modular symbols in Iwasawa theory
• A torsion Jacquet--Langlands correspondence
• On the Eisenstein ideal for imaginary quadratic fields
• A reciprocity map and the two variable p-adic L-function
• The Steinberg Symbol and Special Values of L-functions

Cited by

• Localization and elliptic motivic relations

Related

• Eisenstein cohomology classes for GL_N over imaginary quadratic fields
• Cocycles de groupe pour GL_n et arrangements d'hyperplans
• Two results on Eisenstein part of homology and cohomology groups of Bianchi modular groups
• On the Selmer groups and Mordell-Weil groups of elliptic curves y² = x (x ± p) (x ± q) over imaginary quadratic number fields of class number one
• Abelian threefolds with imaginary multiplication