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Title: Wonderful Arithmetic Geometry Book
Review: This Book is a cornerstone in Arithmetic Geometry.It is the first time in a single Book so differentarguments find a common place.Let me say that the idea of dividing the work intothree parts,depending on the approach, is entirelynew. In fact,Part 1 starts with elementary theory & applications(primes,diophantine equations& approx)Part 2 gives an account of recent ideas and theory(ch.3:Logic & Recursion, with a sketch of proof ofMatiyasevic's Theorem;ch.4:Algebraic NumberTheory;ch.5:Arithmetic of Algebraic Varieties;ch.6: dealswith Zeta functions and modular forms;ch.7:gives apicture, complete indeed, of Wiles'proof of FermatLast Theorem)Part 3 gives "Analogies and Visions",i.e. the linkbetween numbers fields and function fields(usuallythis analogy is only admitted, but never explainedin other books) and other analogies involving manyrecent arguments in Arithmetic Geometry (such as :Schottky uniformization, Arakelov Geometry, Zetas,Dynamics and Cohomology).
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