國立虎尾科技大學 |

The Absolute Galois Group of a Semi-Local Field

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The Absolute Galois Group of a Semi-Local Field/ by Dan Haran, Moshe Jarden.
作者:	Haran, Dan.
其他作者:	Jarden, Moshe.
面頁冊數:	XVI, 137 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Algebra. -
電子資源:	https://doi.org/10.1007/978-3-030-89191-6
ISBN:	9783030891916

The Absolute Galois Group of a Semi-Local Field
Haran, Dan.

The Absolute Galois Group of a Semi-Local Field[electronic resource] /by Dan Haran, Moshe Jarden. - 1st ed. 2021. - XVI, 137 p.online resource. - Springer Monographs in Mathematics,2196-9922. - Springer Monographs in Mathematics,.

- Introduction -- 1. Topologies -- 2. Families of Subgroups -- 3. Free Products of Finitely Many Profinite Groups -- 4. Generalized Free Products.-5. Relative Embedding Problems -- 6. Strong Proper Projectivity -- 7. Étale Profinite Subset of Subgr(G) -- 8. Fundamental Result -- 9. Main Result. Bibliography -- Index.

This book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational numbers. Its main result, a theorem proved by the authors and Florian Pop in 2012, describes the absolute Galois group of distinguished semi-local algebraic (and other) extensions of the rational numbers as free products of the free profinite group on countably many generators and local Galois groups. This is an instance of a positive answer to the generalized inverse problem of Galois theory. Adopting both an arithmetic and probabilistic approach, the book carefully sets out the preliminary material needed to prove the main theorem and its supporting results. In addition, it includes a description of Melnikov's construction of free products of profinite groups and, for the first time in book form, an account of a generalization of the theory of free products of profinite groups and their subgroups. The book will be of interest to researchers in field arithmetic, Galois theory and profinite groups.

ISBN: 9783030891916

Standard No.: 10.1007/978-3-030-89191-6doiSubjects--Topical Terms:

579870
Algebra.

LC Class. No.: QA150-272

Dewey Class. No.: 512

The Absolute Galois Group of a Semi-Local Field
LDR:02749nam a22004095i 4500 001 1057530
003 DE-He213
005 20211119130656.0
007 cr nn 008mamaa
008 220103s2021 sz | s |||| 0|eng d
020 $a 9783030891916 $9 978-3-030-89191-6
024 7 $a 10.1007/978-3-030-89191-6 $2 doi
035 $a 978-3-030-89191-6
050 4 $a QA150-272
072 7 $a PBF $2 bicssc
072 7 $a MAT002000 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512 $2 23
100 1 $a Haran, Dan. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1362998
245 1 4 $a The Absolute Galois Group of a Semi-Local Field $h [electronic resource] / $c by Dan Haran, Moshe Jarden.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a XVI, 137 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Springer Monographs in Mathematics, $x 2196-9922
505 0 $a - Introduction -- 1. Topologies -- 2. Families of Subgroups -- 3. Free Products of Finitely Many Profinite Groups -- 4. Generalized Free Products.-5. Relative Embedding Problems -- 6. Strong Proper Projectivity -- 7. Étale Profinite Subset of Subgr(G) -- 8. Fundamental Result -- 9. Main Result. Bibliography -- Index.
520 $a This book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational numbers. Its main result, a theorem proved by the authors and Florian Pop in 2012, describes the absolute Galois group of distinguished semi-local algebraic (and other) extensions of the rational numbers as free products of the free profinite group on countably many generators and local Galois groups. This is an instance of a positive answer to the generalized inverse problem of Galois theory. Adopting both an arithmetic and probabilistic approach, the book carefully sets out the preliminary material needed to prove the main theorem and its supporting results. In addition, it includes a description of Melnikov's construction of free products of profinite groups and, for the first time in book form, an account of a generalization of the theory of free products of profinite groups and their subgroups. The book will be of interest to researchers in field arithmetic, Galois theory and profinite groups.
650 0 $a Algebra. $2 gtt $3 579870
650 0 $a Algebraic geometry. $3 1255324
650 0 $a Field theory (Physics). $3 685987
650 2 4 $a Algebraic Geometry. $3 670184
650 2 4 $a Field Theory and Polynomials. $3 672025
700 1 $a Jarden, Moshe. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 672443
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030891909
776 0 8 $i Printed edition: $z 9783030891923
776 0 8 $i Printed edition: $z 9783030891930
830 0 $a Springer Monographs in Mathematics, $x 1439-7382 $3 1254272
856 4 0 $u https://doi.org/10.1007/978-3-030-89191-6
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)