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E-book
Author Brünjes, Lars

Title Forms of Fermat equations and their zeta functions / Lars Brünjes
Published New Jersey : World Scientific, ©2004

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Description 1 online resource
Contents Preface -- Contents -- 1 -- Introduction -- 2 -- The zeta function -- 3 -- Galois descent -- 4 -- Nonabelian cohomology -- 5 -- Weil cohomology theories and l-adic cohomology -- 6 -- Classification of forms -- 7 -- Forms of the Fermat equation I -- 8 -- Binary cubic equations -- 9 -- Forms of the Fermat equation II -- 10 -- Representations of semidirect products -- 11 -- The l-adic cohomology of Fermat varieties -- 12 -- The zeta function of forms of Fermat equations -- Appendix A -- Appendix B -- Bibliography -- Index
Summary Annotation. 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 I-adic cohomology (and so in particular the zeta function) of the hypersurface associated with an arbitrary form of the Fermat equation is computed
Bibliography Includes bibliographical references and index
Notes English
Subject Functions, Zeta.
Fermat numbers.
MATHEMATICS -- Calculus.
MATHEMATICS -- Mathematical Analysis.
Fermat numbers
Functions, Zeta
Form Electronic book
ISBN 9812561803
9789812561800
9789812560391
9812560394
1281872091
9781281872098
9786611872090
6611872094