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The main topic is the study of forms of the Fermat equation over an arbitrary field K. Using Galois descent, all such forms are classified; particularly, a complete and explicit classification of all cubic binary equations is given. If K is a finite field containing the d-th roots of unity, the Galois representation on l-adic cohomology (and so in particular the zeta function) of the hypersurface associated with an arbitrary form of the Fermat equation of degree d is computed.
Diophantus and diophantine equations Автор: Isabella G. Bashmakova Год: 1998 |
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Exploratory Galois Theory Автор: Swallow J. Год: 2004 |
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