# Around abelian schemes over the integers

This is the transcription to blog format of a talk I gave at the UC Berkeley Student Arithmetic Geometry Seminar about several topics related to Fontaine’s famous result that there are no abelian schemes over $\mathbb{Z}$.

# Maps from simply connected projective varieties to curves

In this post we prove a general result that shows, in particular, that any map from a simply connected $X$ to a curve $C$ of genus at least $1$ is constant.

# Local class field theory: a discussion

In this post we discuss local class field theory (specifically looking at $p$-adic fields) with a focus on the broader picture, and the multiple approaches.

# 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.