In this post we compute the Galois representation where is the natural inclusion and is the inclusion of the origin.
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.
In this post we compute the group where is a number field.
In this post we compute the compactly supported cohomology of some simple varieties.
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.
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.