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.

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Some examples of Geometric Galois representations

In this post we discuss the Galois representation associated to a projective scheme X/K, where K is a number field. We also discuss how this representation can be computed in several simple cases.

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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.

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