Automorphism group scheme

Algebraic affine group scheme 24 Algebraic matrix group 29 Anisotropic torus 56 Anti-equivalence 15 Antipode 8 Arf invariant 147 Artin-Schreier theory 143 Augmentation ideal 13 Automorphism group scheme 58... 

Theorem. Finite etale group schemes over k are equivalent to finite groups where is acting continuously as group automorphisms. 

Theorem. Let G be a connected affine group scheme acting as automorphisms of an algebraic group scheme T of multiplicative type. Then G acts trivially. 

Other abelian group schemes of course can have connected groups of automorphisms on G , for instance, G acts by xt— ax. 

Let A be a field, and G a finite fc-group scheme. Let S = Speci be an affine fc-scheme of finite type with a left G-action. It gives a A -algebra automorphism action of G on R. Let A = be the ring of invariants. 

---