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 a positive integer. We show that that the finite simple groups of Lie type if and appear as Galois groups over , for some divisible by . 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 .
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 un entier positif. Nous montrons que les groupes finis simples de type de Lie lorsque et sont des groupes de Galois sur pour un entier divisant . 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 .
Chandrashekhar Khare 1; Michael Larsen 2; Gordan Savin 3
@article{AFST_2010_6_19_1_37_0, 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}, year = {2010}, doi = {10.5802/afst.1235}, mrnumber = {2597780}, zbl = {1194.11063}, language = {en}, url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1235/} }
TY - JOUR AU - Chandrashekhar Khare AU - Michael Larsen AU - Gordan Savin TI - Functoriality and the Inverse Galois problem II: groups of type $B_n$ and $G_2$ JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2010 SP - 37 EP - 70 VL - 19 IS - 1 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1235/ DO - 10.5802/afst.1235 LA - en ID - AFST_2010_6_19_1_37_0 ER -
%0 Journal Article %A Chandrashekhar Khare %A Michael Larsen %A Gordan Savin %T Functoriality and the Inverse Galois problem II: groups of type $B_n$ and $G_2$ %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2010 %P 37-70 %V 19 %N 1 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1235/ %R 10.5802/afst.1235 %G en %F AFST_2010_6_19_1_37_0
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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