In this post we compute the Galois representation where is the natural inclusion and is the inclusion of the origin.

# etale cohomology

# 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.

# A computation a day: the Brauer group of a number ring

In this post we compute the group where is a number field.

# A computation a day: compactly supported cohomology

In this post we compute the compactly supported cohomology of some simple varieties.

# Some examples of Geometric Galois representations

In this post we discuss the Galois representation associated to a projective scheme , where 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.