Read the section 6 on complete varieties (pages 45-46) and prepare to discuss Proposition 6.1.

Read and prepare the proof that P^n is complete.

Learn the definition of G_m, G_a, GL(n), SL(n), O(n), SO(n), Sp(2m) as algebraic groups. In each case, describe the morphism from A to A\otimes_k A that is dual to the multiplication mu:GxG->G, where G = Spec(A).

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.