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Heights in Diophantine Geometry(2006)
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Bombieri & Gubler
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Cambridge
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1 edition
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674 pages
ISBN
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0521846153
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Diophantine geometry has been studied by number theorists for thousands of years, since the time of Pythagoras, and has continued to be a rich area of ideas such as Fermat's Last Theorem, and most recently the ABC conjecture. This monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The authors provide a clear path through the subject for graduate students and researchers. They have re-examined many results and much of the literature, and provide a thorough account of several topics at a level not seen before in book form. The treatment is largely self-contained, with proofs given in full detail.
1.Heights
2.Weil heights
3.Linear tori
4.Small points
5.The unit equation
6.Roth's theorem
7.The subspace theorem
8.Abelian varieties
9.Neron-tate heights
10.The mordell-weil theorem
11.Faltings's theorem
12.The abs-conjecture
13.Nevanlinna theory
14.The vojta conjectures
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