Level compatibility in Sharifi's conjecture

Emmanuel Lecouturier, Jun Wang

Sharifi has constructed a map from the first homology of the modular curve $X_1(M)$ to the $K$-group $K_2(\mathbf{Z}[{\zeta }_M,\frac{1}{M}])$, where ${\zeta }_M$ is a primitive $M$th root of u…