Download or read book Algebraic Patching written by Moshe Jarden and published by Springer Science & Business Media. This book was released on 2011-01-03 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming only basic algebra and Galois theory, the book develops the method of "algebraic patching" 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 "ample fields". Among others, it leads to the solution of two central results in "Field Arithmetic": (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 $C$.