I collect here some expository notes.

  1. Notes from a talk on the Hilbert-Mumford criterion. A proof of the Hilbert-Mumford criterion in the projective-over-affine setting is sketched. (pdf)

  2. Linearly reductive algebraic groups in characteristic 0. An expository account of the equivalence between reductivity and linear reductivity in characteristic 0. It also contains a proof of finite generation of the ring of invariants. (pdf)

  3. The absolute Galois group of C(t) (in french). An exposition of a proof that the absolute Galois group of C(t) is isomorphic to the free profinite group on the set of complex numbers. (pdf)