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The Mordell Conjecture - A Complete Proof from Diophantine Geometry (Hardcover, New Ed)
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The Mordell Conjecture - A Complete Proof from Diophantine Geometry (Hardcover, New Ed)
Series: Cambridge Tracts in Mathematics
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The Mordell conjecture (Faltings's theorem) is one of the most
important achievements in Diophantine geometry, stating that an
algebraic curve of genus at least two has only finitely many
rational points. This book provides a self-contained and detailed
proof of the Mordell conjecture following the papers of Bombieri
and Vojta. Also acting as a concise introduction to Diophantine
geometry, the text starts from basics of algebraic number theory,
touches on several important theorems and techniques (including the
theory of heights, the Mordell-Weil theorem, Siegel's lemma and
Roth's lemma) from Diophantine geometry, and culminates in the
proof of the Mordell conjecture. Based on the authors' own teaching
experience, it will be of great value to advanced undergraduate and
graduate students in algebraic geometry and number theory, as well
as researchers interested in Diophantine geometry as a whole.
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