2012/03/31 by Sara Arias-de-Reyna, Luis Dieulefait, Gabor Wiese · 2 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #Differential Galois theory #Dimension (graph theory) #Embedding problem #Galois extension #Galois group #Galois module #Normal basis #Polynomial and algebraic computation #Symplectic geometry #Symplectic group #math.NT #msc:11F80 #msc:12F12 #msc:20G14
paper · pdf · doi:10.2140/pjm.2016.281.1
published in Pacific Journal of Mathematics 281(1), 1-16 (Mathematical Sciences Publishers) · 14 pages; the proof of the classification result has been significantly shortened by appealing to results of Kantor
arxiv created 2014/05/06 · openalex publication_date 2016/02/09 · arxiv updated 2016/02/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
This article is the second part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part is concerned with symplectic Galois representations having a huge residual image, by which we mean that a symplectic group of full dimension over the prime field is contained up to conjugation. A key ingredient is a classification of symplectic representations whose image contains a nontrivial transvection: these fall into three very simply describable classes, the reducible ones, the induced ones and those with huge image. Using the idea of an (n,p)-group of Khare, Larsen and Savin we give simple conditions under which a symplectic Galois representation with coefficients in a finite field has a huge image. Finally, we combine this classification result with the main result of the first part to obtain a strenghtened application to the inverse Galois problem.