UCLA

This dissertation details the construction of the map $\Upsilon$ of Sharifi's conjecture for a general tame level $N$ and odd prime $p$ satisfying $Np > 3$ and for general non-exceptional characters $\theta$ of $(\Z/Np\Z)^\times$. We then show that, conditioned upon a certain Zariski density result of Hida, the constructed map $\Upsilon$ is in fact surjective and is an isomorphism modulo $p$-torsion.