Dansk
Jarden, Moshe
(forfatter)
Algebraic Patching e-bog
436,85 DKK
Assuming only basic algebra and Galois theory, the book develops the method of "e;algebraic patching"e; to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "e;ample fields"e;. Among others, it leads to the solution of two central results in "e;Field Arithmetic…
Assuming only basic algebra and Galois theory, the book develops the method of "e;algebraic patching"e; to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "e;ample fields"e;. Among others, it leads to the solution of two central results in "e;Field Arithmetic"e;: (a) The absolute Galois group of a countable Hilbertian pac field is free on countably many generators; (b) The absolute Galois group of a function field of one variable over an algebraically closed field $C$ is free of rank equal to the cardinality of $C$.
E-bog
436,85 DKK
Forlag
Springer
Udgivet
03.01.2011
Genrer
PBF
Sprog
English
Format
pdf
Beskyttelse
LCP
ISBN
9783642151286
Assuming only basic algebra and Galois theory, the book develops the method of "e;algebraic patching"e; to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "e;ample fields"e;. Among others, it leads to the solution of two central results in "e;Field Arithmetic"e;: (a) The absolute Galois group of a countable Hilbertian pac field is free on countably many generators; (b) The absolute Galois group of a function field of one variable over an algebraically closed field $C$ is free of rank equal to the cardinality of $C$.