Geodesic
Outer forms of type $A_{2}$ with infinite genus
Documenta mathematica, Tome 29 (2024) no. 4, pp. 805-814

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Let G be an absolutely almost simple algebraic group over a field K. The genus genK​(G) of G is the set of K-isomorphism classes of K-forms G′ of G that have the same K-isomorphism classes of maximal K-tori as G. We construct an example of outer forms of type A2​ with infinite genus.
DOI : 10.4171/dm/963
Classification : 16K20, 20G15
Mots-clés : division algebra, algebraic group, genus, maximal subfield of a division algebra, algebra with involution 
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     author = {Sergey V. Tikhonov},
     title = {Outer forms of type $A_{2}$ with infinite genus},
     journal = {Documenta mathematica},
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     publisher = {mathdoc},
     volume = {29},
     number = {4},
     year = {2024},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/963/}
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Sergey V. Tikhonov. Outer forms of type $A_{2}$ with infinite genus. Documenta mathematica, Tome 29 (2024) no. 4, pp. 805-814. doi: 10.4171/dm/963

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