Galois Representations Associated to $p$-adic Families of Modular Forms of Finite Slope

Tomoki Mihara

We define a pro-$p$ Abelian sheaf on a modular curve of a fixed level $N\ge 5$ divisible by a prime number $p\ne 2$. Every $p$-adic representation of $\text{Gal}(\overline{\mat…