Author: alexyoucis

Shimura Varieties: motivation

This will be the first in a series of posts discussing Shimura varieties. In particular, we will focus here on a sort of broad motivation for the subject—why Shimura varieties are a natural thing to study and, in particular, what they give us.


Kummer theory and the weak Mordell-Weil theorem

In this post we discuss the notion of Kummer theory in its general form, and how this leads to a proof of the (weak) Mordell-Weil theorem.


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.