LEADER 03233nam 22006375 450 001 9910510575803321 005 20251113182642.0 010 $a3-030-89191-7 024 7 $a10.1007/978-3-030-89191-6 035 $a(CKB)5100000000115915 035 $a(MiAaPQ)EBC6858812 035 $a(Au-PeEL)EBL6858812 035 $a(PPN)259385468 035 $a(OCoLC)1287922823 035 $a(DE-He213)978-3-030-89191-6 035 $a(EXLCZ)995100000000115915 100 $a20211119d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Absolute Galois Group of a Semi-Local Field /$fby Dan Haran, Moshe Jarden 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (147 pages) 225 1 $aSpringer Monographs in Mathematics,$x2196-9922 311 08$a3-030-89190-9 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThis book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational numbers. Its main result, a theorem proved by the authors and Florian Pop in 2012, describes the absolute Galois group of distinguished semi-local algebraic (and other) extensions of the rational numbers as free products of the free profinite group on countably many generators and local Galois groups. This is an instance of a positive answer to the generalized inverse problem of Galois theory. Adopting both an arithmetic and probabilistic approach, the book carefully sets out the preliminary material needed to prove the main theorem and its supporting results. In addition, it includes a description of Melnikov's construction of free products of profinite groups and, for the first time in book form, an account of a generalization of the theory of free products of profinite groups and their subgroups. The book will be of interest to researchers in fieldarithmetic, Galois theory and profinite groups. 410 0$aSpringer Monographs in Mathematics,$x2196-9922 606 $aAlgebra 606 $aAlgebraic geometry 606 $aAlgebraic fields 606 $aPolynomials 606 $aAlgebra 606 $aAlgebraic Geometry 606 $aField Theory and Polynomials 615 0$aAlgebra. 615 0$aAlgebraic geometry. 615 0$aAlgebraic fields. 615 0$aPolynomials. 615 14$aAlgebra. 615 24$aAlgebraic Geometry. 615 24$aField Theory and Polynomials. 676 $a512.32 700 $aHaran$b Dan$0865027 702 $aJarden$b Moshe 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910510575803321 996 $aThe absolute Galois group of a semi-local field$92786315 997 $aUNINA