Electronic ISBN:  9780821877777 
Product Code:  CONM/186.E 
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Book DetailsContemporary MathematicsVolume: 186; 1995; 401 ppMSC: Primary 12; 20; 11;
This book contains the refereed proceedings of the AMSIMSSIAM Joint Summer Research Conference on Recent Developments in the Inverse Galois Problem, held in July 1993 at the University of Washington, Seattle. A new review of Serre's
Topics in Galois Theory serves as a starting point. The book describes the latest research on explicit presentation of the absolute Galois group of the rationals. Containing the first appearance of generalizations of modular curves, the book presents applications that demonstrate the full scope of the Inverse Galois Problem. In particular, the papers collected here show the ubiquity of the applications of the Inverse Galois Problem and its compelling significance. The book will serve as a guide to progress on the Inverse Galois Problem and as an aid in using this work in other areas of mathematics. This includes coding theory and other finite field applications. Group theory and a first course in algebraic curves are sufficient for understanding many papers in the volume. Graduate students will find this an excellent reference to current research, as it contains a list of problems appropriate for thesis material in arithmetic geometry, algebraic number theory, and group theory.ReadershipResearchers in number theory and group theory and students seeking applications of pure mathematics as downtoearth problems.

Table of Contents

Part A: Explicit Quotients of $G_{\mathbb {Q}}$ and $G_{\bar {\mathbb {F}}(t)}$ [ MR 1352262 ]

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 ${\bf Q}$ [ 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 ${\bf P}^1$ and Galois action on their division points [ MR 1352269 ]

Part B: Moduli Spaces and the Structure of $G_{\mathbb {Q}}$ [ MR 1352262 ]

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 $G_{\mathbb {Q}_p(t)}$ [ MR 1352262 ]

Pierre Dèbes  Covers of ${\bf P}^1$ 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 ${\bf Q}_p(T)$, 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 ${\bf P}^1\times {\bf P}^1\times {\bf P}^1$ [ MR 1352278 ]

Part D: Group Theory and Geometric Monodromy Groups [ MR 1352262 ]

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 ]


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This book contains the refereed proceedings of the AMSIMSSIAM Joint Summer Research Conference on Recent Developments in the Inverse Galois Problem, held in July 1993 at the University of Washington, Seattle. A new review of Serre's
Researchers in number theory and group theory and students seeking applications of pure mathematics as downtoearth problems.

Part A: Explicit Quotients of $G_{\mathbb {Q}}$ and $G_{\bar {\mathbb {F}}(t)}$ [ MR 1352262 ]

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 ${\bf Q}$ [ 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 ${\bf P}^1$ and Galois action on their division points [ MR 1352269 ]

Part B: Moduli Spaces and the Structure of $G_{\mathbb {Q}}$ [ MR 1352262 ]

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 $G_{\mathbb {Q}_p(t)}$ [ MR 1352262 ]

Pierre Dèbes  Covers of ${\bf P}^1$ 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 ${\bf Q}_p(T)$, 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 ${\bf P}^1\times {\bf P}^1\times {\bf P}^1$ [ MR 1352278 ]

Part D: Group Theory and Geometric Monodromy Groups [ MR 1352262 ]

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 ]