This book is intended to be an introduction to Diophantine geometry. The central theme of the book is to investigate the distribution of integral points on algebraic varieties. This text rapidly introduces problems in Diophantine geometry, especially those involving integral points, assuming a geometrical perspective. It presents recent results not available in textbooks and also new viewpoints on classical material. In some instances, proofs have been replaced by a detailed analysis of particular cases, referring to the quoted papers for complete proofs. A central role is played by Siegel’s finiteness theorem for integral points on curves. The book ends with the analysis of integral points on surfaces.
Зміст
Chapter 1. Integral points on algebraic varieties.-
Chapter 2. Diophantine approximation.-
Chapter 3. The theorems of Thue and Siegel.-
Chapter 4. Hilbert Irreducibility Theorem.-
Chapter 5. Integral points on surfaces.
Про автора
Pietro Corvaja is full professor of geometry at the Dipartimento Di Mathematica Einformatica at the Universita’ degli studi di udine, Italy. His research topics are arithmetic geometry, Diophantine approximation and the theory of transcendental numbers.
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