# p-divisible groups, formal groups, and the Serre-Tate theorem

In this post we discuss the basic theory of p-divisible groups, their relationship to formal groups, and the Serre-Tate theorem.

# 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.

# 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 $p$.

# 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.