Progress in Galois Theory: Proceedings of John Thompson's 70th Birthday Conference (Developments in Mathematics)

0 avg rating
( 0 ratings by Goodreads )
 
9780387235332: Progress in Galois Theory: Proceedings of John Thompson's 70th Birthday Conference (Developments in Mathematics)

The legacy of Galois was the beginning of Galois theory as well as group theory. From this common origin, the development of group theory took its own course, which led to great advances in the latter half of the 20th cen­ tury. It was John Thompson who shaped finite group theory like no-one else, leading the way towards a major milestone of 20th century mathematics, the classification of finite simple groups. After the classification was announced around 1980, it was again J. Thomp­ son who led the way in exploring its implications for Galois theory. The first question is whether all simple groups occur as Galois groups over the rationals (and related fields), and secondly, how can this be used to show that all finite groups occur (the 'Inverse Problem of Galois Theory'). What are the implica­ tions for the stmcture and representations of the absolute Galois group of the rationals (and other fields)? Various other applications to algebra and number theory have been found, most prominently, to the theory of algebraic curves (e.g., the Guralnick-Thompson Conjecture on the Galois theory of covers of the Riemann sphere).

"synopsis" may belong to another edition of this title.

From the Back Cover:

A recent trend in the field of Galois theory is to tie the previous theory of curve coverings (mostly of the Riemann sphere) and Hurwitz spaces (moduli spaces for such covers) with the theory of algebraic curves and their moduli spaces. A general survey of this is given in the article by Voelklein. Further exemplifications come in the articles of Guralnick on automorphisms of modular curves in positive characteristic, of Zarhin on the Galois module structure of the 2-division points of hyperelliptic curves and of Krishnamoorthy, Shashka and Voelklein on invariants of genus 2 curves.

Abhyankar continues his work on explicit classes of polynomials in characteristic p>0 whose Glaois groups comprise entire families of Lie type groups in characteristic p. In his article, he proves a characterization of sympletic groups required for the identification of the Galois group of certain polynomials. 

The more abstract aspects come into play when considering the totality of Galois extensions of a given field.  This leads to the study of absolute Galois groups and (profinite) fundamental groups. Haran and Jarden present a result on the problem of finding a group-theoretic characterization of absolute Galois groups. In a similar spirit, Boston studies infinite p-extensions of number fields unramified at p and makes a conjecture about a group-theoretic characterization of their Galois groups. He notes connections with the Fontaine-Mazur conjecture, knot theory and quantum field theory.  Nakamura continues his work on relationships between the absolute Galois group of the rationals and the Grothendieck-Teichmüller group. Finally, Fried takes us on a tour of places where classical tropics like modular curves and j-line covers connect to the genus zero problems which was the starting point of the Guralnick-Thompson Conjecture.

Audience

This volume is suitable for graduate students and researchers in the field.

"About this title" may belong to another edition of this title.

Top Search Results from the AbeBooks Marketplace

1.

Published by Springer
ISBN 10: 0387235337 ISBN 13: 9780387235332
New Hardcover Quantity Available: 1
Seller:
Secondsource Books Inc.
(Bolton, ON, Canada)
Rating
[?]

Book Description Springer. Hardcover. Book Condition: New. 0387235337 **New** copy, unmarked EXCELLENT condition; ships USPS with delivery confirmation in US 931AA. Bookseller Inventory # SKU1092179

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 48.03
Convert Currency

Add to Basket

Shipping: US$ 3.99
From Canada to U.S.A.
Destination, Rates & Speeds

2.

Published by Springer (2004)
ISBN 10: 0387235337 ISBN 13: 9780387235332
New Hardcover Quantity Available: 1
Seller:
Irish Booksellers
(Rumford, ME, U.S.A.)
Rating
[?]

Book Description Springer, 2004. Hardcover. Book Condition: New. book. Bookseller Inventory # M0387235337

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 69.57
Convert Currency

Add to Basket

Shipping: FREE
Within U.S.A.
Destination, Rates & Speeds

3.

Voelklein, Helmut
Published by Springer (2016)
ISBN 10: 0387235337 ISBN 13: 9780387235332
New Paperback Quantity Available: 1
Print on Demand
Seller:
Ria Christie Collections
(Uxbridge, United Kingdom)
Rating
[?]

Book Description Springer, 2016. Paperback. Book Condition: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Bookseller Inventory # ria9780387235332_lsuk

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 187.58
Convert Currency

Add to Basket

Shipping: US$ 5.11
From United Kingdom to U.S.A.
Destination, Rates & Speeds

4.

Helmut Voelklein
Published by Springer-Verlag New York Inc. (2004)
ISBN 10: 0387235337 ISBN 13: 9780387235332
New Quantity Available: > 20
Print on Demand
Seller:
Pbshop
(Wood Dale, IL, U.S.A.)
Rating
[?]

Book Description Springer-Verlag New York Inc., 2004. HRD. Book Condition: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # IP-9780387235332

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 193.79
Convert Currency

Add to Basket

Shipping: US$ 3.99
Within U.S.A.
Destination, Rates & Speeds

5.

HELMUT VOELKLEIN
Published by Springer (2004)
ISBN 10: 0387235337 ISBN 13: 9780387235332
New Hardcover Quantity Available: 1
Seller:
Herb Tandree Philosophy Books
(Stroud, GLOS, United Kingdom)
Rating
[?]

Book Description Springer, 2004. Hardback. Book Condition: NEW. 9780387235332 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Bookseller Inventory # HTANDREE0272070

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 200.41
Convert Currency

Add to Basket

Shipping: US$ 10.56
From United Kingdom to U.S.A.
Destination, Rates & Speeds

6.

Helmut Voelklein
Published by Springer-Verlag New York Inc. (2004)
ISBN 10: 0387235337 ISBN 13: 9780387235332
New Quantity Available: > 20
Print on Demand
Seller:
Books2Anywhere
(Fairford, GLOS, United Kingdom)
Rating
[?]

Book Description Springer-Verlag New York Inc., 2004. HRD. Book Condition: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Bookseller Inventory # IP-9780387235332

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 202.60
Convert Currency

Add to Basket

Shipping: US$ 11.88
From United Kingdom to U.S.A.
Destination, Rates & Speeds

7.

Published by Springer
ISBN 10: 0387235337 ISBN 13: 9780387235332
New Quantity Available: 1
Print on Demand
Seller:
Majestic Books
(London, ,, United Kingdom)
Rating
[?]

Book Description Springer. Book Condition: New. pp. x + 168 This item is printed on Demand. Bookseller Inventory # 7597022

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 225.93
Convert Currency

Add to Basket

Shipping: US$ 7.26
From United Kingdom to U.S.A.
Destination, Rates & Speeds

8.

Voelklein, Helmut [Editor]; Shaska, Tanush [Editor];
Published by Springer (2004)
ISBN 10: 0387235337 ISBN 13: 9780387235332
New Hardcover Quantity Available: 10
Seller:
Ergodebooks
(RICHMOND, TX, U.S.A.)
Rating
[?]

Book Description Springer, 2004. Hardcover. Book Condition: New. Bookseller Inventory # INGM9780387235332

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 234.72
Convert Currency

Add to Basket

Shipping: US$ 4.99
Within U.S.A.
Destination, Rates & Speeds

9.

Published by Springer-Verlag New York Inc., United States (2005)
ISBN 10: 0387235337 ISBN 13: 9780387235332
New Hardcover Quantity Available: 10
Print on Demand
Seller:
The Book Depository US
(London, United Kingdom)
Rating
[?]

Book Description Springer-Verlag New York Inc., United States, 2005. Hardback. Book Condition: New. 2005 ed.. Language: English . Brand New Book ***** Print on Demand *****. The legacy of Galois was the beginning of Galois theory as well as group theory. From this common origin, the development of group theory took its own course, which led to great advances in the latter half of the 20th cen- tury. It was John Thompson who shaped finite group theory like no-one else, leading the way towards a major milestone of 20th century mathematics, the classification of finite simple groups. After the classification was announced around 1980, it was again J. Thomp- son who led the way in exploring its implications for Galois theory. The first question is whether all simple groups occur as Galois groups over the rationals (and related fields), and secondly, how can this be used to show that all finite groups occur (the Inverse Problem of Galois Theory ). What are the implica- tions for the stmcture and representations of the absolute Galois group of the rationals (and other fields)? Various other applications to algebra and number theory have been found, most prominently, to the theory of algebraic curves (e.g., the Guralnick-Thompson Conjecture on the Galois theory of covers of the Riemann sphere). Bookseller Inventory # APC9780387235332

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 240.62
Convert Currency

Add to Basket

Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

10.

Published by Springer-Verlag New York Inc., United States (2005)
ISBN 10: 0387235337 ISBN 13: 9780387235332
New Hardcover Quantity Available: 10
Print on Demand
Seller:
The Book Depository
(London, United Kingdom)
Rating
[?]

Book Description Springer-Verlag New York Inc., United States, 2005. Hardback. Book Condition: New. 2005 ed.. Language: English . Brand New Book ***** Print on Demand *****.The legacy of Galois was the beginning of Galois theory as well as group theory. From this common origin, the development of group theory took its own course, which led to great advances in the latter half of the 20th cen- tury. It was John Thompson who shaped finite group theory like no-one else, leading the way towards a major milestone of 20th century mathematics, the classification of finite simple groups. After the classification was announced around 1980, it was again J. Thomp- son who led the way in exploring its implications for Galois theory. The first question is whether all simple groups occur as Galois groups over the rationals (and related fields), and secondly, how can this be used to show that all finite groups occur (the Inverse Problem of Galois Theory ). What are the implica- tions for the stmcture and representations of the absolute Galois group of the rationals (and other fields)? Various other applications to algebra and number theory have been found, most prominently, to the theory of algebraic curves (e.g., the Guralnick-Thompson Conjecture on the Galois theory of covers of the Riemann sphere). Bookseller Inventory # APC9780387235332

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 248.34
Convert Currency

Add to Basket

Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

There are more copies of this book

View all search results for this book