Forms Of Fermat Equations And Their Zeta Functions
by
Lars Brunjes
Book Details
Format
Hardback or Cased Book
ISBN-10
9812560394
ISBN-13
9789812560391
Publisher
World Scientific Publishing Co Pte Ltd
Imprint
World Scientific Publishing Co Pte Ltd
Country of Manufacture
SG
Country of Publication
GB
Publication Date
Oct 19th, 2004
Print length
248 Pages
Weight
550 grams
Dimensions
15.70 x 23.00 x 2.00 cms
Product Classification:
Number theory
Ksh 17,800.00
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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.
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.
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