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Recent Developments in the Inverse Galois Problem

About this Title

Michael D. Fried, Shreeram S. Abhyankar, Walter Feit, Yasutaka Ihara and Helmut Voelklein, Editors

Publication: Contemporary Mathematics
Publication Year: 1995; Volume 186
ISBNs: 978-0-8218-0299-1 (print); 978-0-8218-7777-7 (online)
DOI: https://doi.org/10.1090/conm/186
MathSciNet review: 1352262

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Table of Contents

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Front/Back Matter

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Part A: Explicit Quotients of $G_{\mathbb {Q}}$ and $G_{\bar {\mathbb {F}}(t)}$

• Teresa Crespo – Explicit Galois realization of $C_{16}$-extensions of $A_n$ and $S_n$ [MR 1352263]
• Michael D. Fried – Review of: Topics in Galois theory [Jones and Bartlett, Boston, MA, 1992; MR1162313 (94d:12006)] by J.-P. Serre [MR 1352264]
• B. H. Matzat – Parametric solutions of embedding problems [MR 1352265]
• Amadeu Reverter and Núria Vila – Some projective linear groups over finite fields as Galois groups over $\textbf {Q}$ [MR 1352266]
• Steven Liedahl and Jack Sonn – $K$-admissibility of metacyclic $2$-groups [MR 1352267]
• John R. Swallow – Embedding problems and the $C_{16}\to C_8$ obstruction [MR 1352268]
• Helmut Völklein – Cyclic covers of $\textbf {P}^1$ and Galois action on their division points [MR 1352269]

Part B: Moduli Spaces and the Structure of $G_{\mathbb {Q}}$

• Michael D. Fried – Introduction to modular towers: generalizing dihedral group–modular curve connections [MR 1352270]
• Yasutaka Ihara and Makoto Matsumoto – On Galois actions on profinite completions of braid groups [MR 1352271]
• Makoto Matsumoto – On the Galois image in the derivation algebra of $\pi _1$ of the projective line minus three points [MR 1352272]

Part C: The Structure of $G_{\mathbb {R}(t)}$, $G_{\bar {\mathbb {F}}(t)}$, and $G_{\mathbb {Q}_p(t)}$

• Pierre Dèbes – Covers of $\textbf {P}^1$ over the $p$-adics [MR 1352273]
• Bruno Deschamps – Existence de points $p$-adiques pour tout $p$ sur un espace de Hurwitz [MR 1352274]
• Eric Dew – Stable models [MR 1352275]
• Qing Liu – Tout groupe fini est un groupe de Galois sur $\textbf {Q}_p(T)$, d’après Harbater [MR 1352276]
• Wolfgang K. Seiler – Specializations of coverings and their Galois groups [MR 1352277]
• Lan Wang – Rational points and canonical heights on $K3$-surfaces in $\textbf {P}^1\times \textbf {P}^1\times \textbf {P}^1$ [MR 1352278]

Part D: Group Theory and Geometric Monodromy Groups

• Shreeram S. Abhyankar – Mathieu group coverings and linear group coverings [MR 1352279]
• Paul Feit – Fundamental groups for arbitrary categories [MR 1352280]
• Robert M. Guralnick and Michael G. Neubauer – Monodromy groups of branched coverings: the generic case [MR 1352281]
• David Harbater – Fundamental groups and embedding problems in characteristic $p$ [MR 1352282]
• Moshe Jarden – On free profinite groups of uncountable rank [MR 1352283]
• Peter Müller – Primitive monodromy groups of polynomials [MR 1352284]