Science/Engineering Cubic Forms: Iu I. Manin (0444878238)

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Cubic Forms: Iu I. Manin

From the introduction:

Every mathematician who is not indifferent to number theory has felt the charm of Fermat's theorem on the sum of two squares of natural numbers. A psychologist of the Jungian school would probably think that such diophantine problems are archetypal to a high degree.

The basic idea for the book presented here arose from an attempt to find out what happens in the case of sums of three rational cubes. Needless to say, the result is not nearly so simple, fundamental and complete as the classical pattern. The author has generalized the problem along all the lines which occurred to him, and has used all technical resources known to him. He obtained as a result the multitude of non-associative composition laws, monoidal transformations and Galois cohomologies which make up this book.

About this book:

Hardbound. Since this book was first published in English, there has been important progress in a number of related topics. The class of algebraic varieties close to the rational ones has crystallized as a natural domain for the methods developed and expounded in this volume. For this revised edition, the original text has been left intact (except for a few corrections) and has been brought up to date by the addition of an Appendix and recent references.

The Appendix sketches some of the most essential new results, constructions and ideas, including the solutions of the Luroth and Zariski problems, the theory of the descent and obstructions to the Hasse principle on rational varieties, and recent applications of K-theory to arithmetic.

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	Science/Engineering S. I. Gelfand, Yuri I. Manin - Methods of Homological Algebra S. I. Gelfand, Yuri I. Manin - Methods of Homological AlgebraSpringer-Verlag Telos \| 1996 \| ISBN: 3540547460 \| Pages: 372 \| DJVU \| 3.39 MBProvides the modern approach to homological algebra, based on the systematic use of language and ideas ...
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