Local class field theory: a discussion

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

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.

Hodge Symmetry in characteristic Zero

In this post we prove that varieties over characteristic fields are all ‘Hodge symmetric’, meaning that .