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 $C$.
General
| Imprint: |
Springer-Verlag
|
| Country of origin: |
Germany |
| Series: |
Springer Monographs in Mathematics |
| Release date: |
2011 |
| First published: |
2011 |
| Authors: |
Moshe Jarden
|
| Dimensions: |
235 x 155 x 22mm (L x W x T) |
| Format: |
Hardcover
|
| Pages: |
292 |
| Edition: |
2011 Ed. |
| ISBN-13: |
978-3-642-15127-9 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Algebra >
Groups & group theory
|
| LSN: |
3-642-15127-2 |
| Barcode: |
9783642151279 |
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