Realizing cyclic linear transformations as Frobenius elements in the Galois groups of q-polynomials over function fields

2023/09/02 by Gow, Rod, McGuire, Gary
#11R58 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2309.00880

Abstract

We realize Frobenius conjugacy classes in Galois groups of certain q-polynomials over \mathbbF_q(t) using specific degree 1 ideals. We combine this with methods from elementary linear algebra and group theory to realize transvections in some linear Galois groups. This enables the Galois group to be identified as a known classical group in several reasonably general cases.

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