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Functoriality and the Inverse Galois problem II: groups of type B n and G 2
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 1, pp. 37-70.

This paper contains an application of Langlands’ functoriality principle to the following classical problem: which finite groups, in particular which simple groups appear as Galois groups over ? Let be a prime and t a positive integer. We show that that the finite simple groups of Lie type B n ( k )=3DSO 2n+1 (𝔽 k ) der if 3,5(mod8) and G 2 ( k ) appear as Galois groups over , for some k divisible by t. In particular, for each of the two Lie types and fixed we construct infinitely many Galois groups but we do not have a precise control of k.

Cet article donne une application du principe de fonctorialité de Langlands au problème classique suivant  : quels groupes finis, en particulier quels groupes simples, apparaissent comme groupes de Galois sur   ? Soit une nombre premier et t un entier positif. Nous montrons que les groupes finis simples de type de Lie B n ( k )=3DSO 2n+1 (𝔽 k ) der lorsque 3,5(mod8) et G 2 ( k ) sont des groupes de Galois sur pour un entier k divisant t. En particulier, pour chacun de ces deux types de Lie et pour un entier fixé, nous construisons une infinité de groupes de Galois, mais nous n’avons pas de contrôle précis sur k.

DOI: 10.5802/afst.1235
Chandrashekhar Khare 1; Michael Larsen 2; Gordan Savin 3

1 Department of Mathematics, UCLA, Los Angeles CA 90095-1555, U.S.A.
2 Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.
3 Department of Mathematics, University of Utah, 155 South 1400 East, Room 233, Salt Lake City, UT 84112-0090, U.S.A
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     author = {Chandrashekhar Khare and Michael Larsen and Gordan Savin},
     title = {Functoriality and the {Inverse} {Galois} problem {II:} groups of type $B_n$ and $G_2$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {37--70},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 19},
     number = {1},
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}
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Chandrashekhar Khare; Michael Larsen; Gordan Savin. Functoriality and the Inverse Galois problem II: groups of type $B_n$ and $G_2$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 1, pp. 37-70. doi : 10.5802/afst.1235. https://afst.centre-mersenne.org/articles/10.5802/afst.1235/

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