# A computation a day: a pullback pushforward

In this post we compute the Galois representation $i^\ast R^m j_\ast\mathbb{Q}_\ell$ where $j:\mathbb{G}_{m,\overline{k}}\hookrightarrow\mathbb{A}^1_k$ is the natural inclusion and $i:\text{Spec}(k)\hookrightarrow \mathbb{A}^1_k$ is the inclusion of the origin.

# A class field theoretic phenomenon

In this post we discuss one example of what’s called a ‘class field theoretic phenomenon’. In particular, we focus on the application of trying to understand the property of when $X^3-2$ has three distinct roots modulo $p$, for various primes $p$.