Algebraic Patching
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&...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2011, 2011
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| Edition: | 1st ed. 2011 |
| Series: | Springer Monographs in Mathematics
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| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
| Summary: | 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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| Physical Description: | XXIV, 292 p online resource |
| ISBN: | 9783642151286 |