03233nam 22006375 450 991051057580332120251113182642.03-030-89191-710.1007/978-3-030-89191-6(CKB)5100000000115915(MiAaPQ)EBC6858812(Au-PeEL)EBL6858812(PPN)259385468(OCoLC)1287922823(DE-He213)978-3-030-89191-6(EXLCZ)99510000000011591520211119d2021 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe Absolute Galois Group of a Semi-Local Field /by Dan Haran, Moshe Jarden1st ed. 2021.Cham :Springer International Publishing :Imprint: Springer,2021.1 online resource (147 pages)Springer Monographs in Mathematics,2196-99223-030-89190-9 Includes bibliographical references and index.- 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 fieldarithmetic, Galois theory and profinite groups.Springer Monographs in Mathematics,2196-9922AlgebraAlgebraic geometryAlgebraic fieldsPolynomialsAlgebraAlgebraic GeometryField Theory and PolynomialsAlgebra.Algebraic geometry.Algebraic fields.Polynomials.Algebra.Algebraic Geometry.Field Theory and Polynomials.512.32Haran Dan865027Jarden MosheMiAaPQMiAaPQMiAaPQBOOK9910510575803321The absolute Galois group of a semi-local field2786315UNINA