Friday April 22

 

  • We will discuss a later result (8.6) from Humphreys: let G be an affine algebraic group over an algebraically closed field k, then G is isomorphic to a closed subgroup of GL(n) (over k) for some n.
  • 7.3. Let G be an affine algebraic group.  Show that G^0 is a normal subgroup of finite index.
  • 7.4. Show that the Zariski closure of a subgroup is a subgroup.
  • 7.4.B. Show that the kernel and images are closed subgroups, and that the image of the connected component of the identity is the connected component of the image.
  • 8.1. State what an action is in the category of k-varieties.
  • Show that GLn acts on P^n, on the flag variety.

We will start on our discussion of elliptic curves as time permits.

 

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