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Recent Developments in the Inverse Galois Problem

Edited by: Shreeram S. Abhyankar Purdue University, West Lafayette, IN
Walter Feit Yale University, New Haven, CT
Michael D. Fried University of California, Irvine, Irvine, CA
Yasutaka Ihara Kyoto University, Kyoto, Japan
Helmut Voelklein University of Florida, Gainesville, FL
Available Formats:
Electronic ISBN: 978-0-8218-7777-7
Product Code: CONM/186.E
List Price: $83.00 MAA Member Price:$74.70
AMS Member Price: $66.40 Click above image for expanded view Recent Developments in the Inverse Galois Problem Edited by: Shreeram S. Abhyankar Purdue University, West Lafayette, IN Walter Feit Yale University, New Haven, CT Michael D. Fried University of California, Irvine, Irvine, CA Yasutaka Ihara Kyoto University, Kyoto, Japan Helmut Voelklein University of Florida, Gainesville, FL Available Formats:  Electronic ISBN: 978-0-8218-7777-7 Product Code: CONM/186.E  List Price:$83.00 MAA Member Price: $74.70 AMS Member Price:$66.40
• Book Details

Contemporary Mathematics
Volume: 1861995; 401 pp
MSC: Primary 12; 20; 11;

This book contains the refereed proceedings of the AMS-IMS-SIAM 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.

Researchers in number theory and group theory and students seeking applications of pure mathematics as down-to-earth 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 ]
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1861995; 401 pp
MSC: Primary 12; 20; 11;

This book contains the refereed proceedings of the AMS-IMS-SIAM 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.

Researchers in number theory and group theory and students seeking applications of pure mathematics as down-to-earth 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 ]
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.