Compatible systems of symplectic Galois representations and the inverse\n Galois problem III. Automorphic construction of compatible systems with\n suitable local properties

2013/08/09 by Sara Arias‐de‐Reyna, Arias-de-Reyna, Sara, Luís Dieulefait +5
Computer Science · Mathematics · #11F80 #12F12 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1308.2192

openalex publication_date 2013/08/09 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

This article is the third and last part of a series of three articles about\ncompatible systems of symplectic Galois representations and applications to the\ninverse Galois problem.\n This part proves the following new result for the inverse Galois problem for\nsymplectic groups. For any even positive integer n and any positive integer d,\nPSp_n(F_l^d) or PGSp_n(F_l^d) occurs as a Galois group over the rational\nnumbers for a positive density set of primes l.\n The result is obtained by showing the existence of a regular, algebraic,\nself-dual, cuspidal automorphic representation of GL_n(A_Q) with local types\nchosen so as to obtain a compatible system of Galois representations to which\nthe results from Part II of this series apply.\n

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