Forms Of Fermat Equations And Their Zeta Functions
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A01=Lars Brunjes
Author_Lars Brunjes
Category=PBH
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Fermat Equation
Fermat Variety
Galois Descent
Higher Degree Forms
Zeta Function
Product details
- ISBN 9789812560391
- Publication Date: 19 Oct 2004
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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In this volume, an abstract theory of 'forms' is developed, thus providing a conceptually satisfying framework for the classification of forms of Fermat equations. The classical results on diagonal forms are extended to the broader class of all forms of Fermat varieties.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.
