# 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 computation a day: the Brauer group of a number ring

In this post we compute the group $\mathrm{Br}(\mathcal{O}_K)$ where $K$ is a number field.

# Some examples of Geometric Galois representations

In this post we discuss the Galois representation associated to a projective scheme $X/K$, where $K$ is a number field. We also discuss how this representation can be computed in several simple cases.

# An invitation to p-adic Hodge theory, or: How i learned to stop worrying and love fontaine

This is the rough outline of a talk I recently gave at the Berkeley Student Algebraic Geometry Seminar on the progression of ideas that might lead one to define the Hodge-Tate decomposition.