2 problems

Let $p$ be a prime number, and let $\k\geqslant 2$ and $N$ be positive integers with $N$ coprime to $p$. For weight $k$ and level $\Gamma_0(Np)$ eigenforms, define the supersingula…

Let $K$ be a number field and let $p$ be a prime number. A continuous Galois representation … is finitely and tamely ramified if it is finitely ramified and tamely ramified. Fontai…