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Fundamentals of Diophantine Geometry


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Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields ...

Fundamentals of Diophantine Geometry 2010, Springer-Verlag New York Inc., New York, NY

ISBN-13: 9781441928184


Fundamentals of Diophantine Geometry 1983, Springer, New York, NY

ISBN-13: 9780387908373

1983 edition