On the image of the Galois representation associated to a non-CM Hida family

Jaclyn Lang

Fix a prime $p>2$. Let $\rho :\text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})\to {\text{GL}}_2(\mathbb{I})$ be the Galois representation coming from a non-CM irreducible component $\mat…