UCLA

This dissertation generalizes work of Sharifi and Venkatesh to construct a canonical choice of cocycle $\Theta$ via a ``lifting" process that represents a cohomology class $$[\Theta] \in H^{n-1}(\mathrm{GL}_n(\mathbb{Z}),K_n^M(\mathbb{Q}(\mathbb{G}_m^n)) \otimes_\mathbb{Z} \mathbb{Z}[\tfrac{1}{(n+1)!}])$$ for an integer $n \geq 2$. We show that $[\Theta]$ is Eisenstein with respect to the action of certain Hecke operators.