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.
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 $C$.
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Develops the method of "algebraic patching" to realize finite groups. Leads to the solution of two central results in "Field Arithmetic". Assumes only basic algebra and Galois theory. Includes supplementary material: sn.pub/extras
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Produktdetaljer
ISBN
9783642151279
Publisert
2011-01-05
Utgiver
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
24
Forfatter