Computation of Hurwitz spaces and new explicit polynomials for almost simple Galois groups

DOI10.1090/mcom/3116zbMath1416.11159arXiv1512.05533OpenAlexW2196878366MaRDI QIDQ2967972

Joachim König

Publication date: 9 March 2017

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.05533

zbMATH Keywords

Galois realizationsalmost simple groupsHurwitz spaces

Mathematics Subject Classification ID

Related Items (4)

Galois realizations with inertia groups of order two ⋮ An approach for computing families of multi-branch-point covers and applications for symplectic Galois groups ⋮ Covering groups of \(M_{22}\) as regular Galois groups over \(\mathbb{Q} \) ⋮ The Grunwald problem and specialization of families of regular Galois extensions

Uses Software

• GAP
• Magma
• BRAID

Cites Work

• Algebraic function fields and codes
• Computation of a cover of Shimura curves using a Hurwitz space
• Polynomials for primitive nonsolvable permutation groups of degree d\(\leq 15\)
• Factoring polynomials with rational coefficients
• The inverse Galois problem and rational points on moduli spaces
• Nonrigid constructions in Galois theory
• The Magma algebra system. I: The user language
• Computation of some moduli spaces of covers and explicit \({\mathcal S}_n\) and \({\mathcal A}_n\) regular \({\mathbb Q}(T)\)-extensions with totally real fibers.
• Numerical calculation of three-point branched covers of the projective line
• Algebraic Patching
• Polynomials with Galois Groups Aut(M 22 ), M 22 , and PSL 3 (\BbbF 4 ) ⋅2 2 Over \BbbQ
• Rigidity and real residue class fields
• A GAP Package for Braid Orbit Computation and Applications
• Construction d'une extension régulière de Q(T) de groupe de Galois M₂₄
• A Database for Field Extensions of the Rationals
• Explicit Galois realization of transitive groups of degree up to 15
• Multi-parameter polynomials with given Galois group
• Boundary of Hurwitz spaces and explicit patching
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