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 .