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Functoriality and the Inverse Galois problem II: groups of type B n and G 2

Chandrashekhar Khare, Michael Larsen, Gordan Savin (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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 ) = 3 D S O 2 n + 1 ( 𝔽 k ) d e r if 3 , 5 ( mod 8 ) 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...

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