Geodesic
Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras
Documenta mathematica, Tome 21 (2016), pp. 917-954

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The question of existence of outer automorphisms of a simple algebraic group G arises naturally both when working with the Galois cohomology of G and as an example of the algebro-geometric problem of determining which connected components of Aut(G) have rational points. The existence question remains open only for four types of groups, and we settle one of the remaining cases, type ^3D_4. The key to the proof is a Skolem-Noether theorem for cubic étale subalgebras of Albert algebras which is of independent interest. Necessary and sufficient conditions for a simply connected group of outer type A to admit outer automorphisms of order 2 are also given.
DOI : 10.4171/dm/549
Classification : 11E72, 17C40, 20G15, 20G41 
Skip Garibaldi; Holger P. Petersson. Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras. Documenta mathematica, Tome 21 (2016), pp. 917-954. doi: 10.4171/dm/549
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     title = {Outer automorphisms of algebraic groups and a {Skolem-Noether} theorem for {Albert} algebras},
     journal = {Documenta mathematica},
     pages = {917--954},
     year = {2016},
     volume = {21},
     doi = {10.4171/dm/549},
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