There's now a lot interaction among reviews on logarithmic varieties and deep elements of mathematics algebraic geometry. New mild has been shed, for example, at the recognized conjectures of Tate and Shafarevich in terms of abelian forms and the linked celebrated discoveries of Faltings developing the Mordell conjecture. This ebook supplies an account of the speculation of linear kinds within the logarithms of algebraic numbers with particular emphasis at the very important advancements of the earlier twenty-five years. the 1st half covers uncomplicated fabric in transcendental quantity concept yet with a latest point of view. the rest assumes a few heritage in Lie algebras and team kinds, and covers, in a few circumstances for the 1st time in booklet shape, a number of complex issues. the ultimate bankruptcy summarises different elements of Diophantine geometry together with hypergeometric conception and the André-Oort conjecture. A accomplished bibliography rounds off this definitive survey of powerful tools in Diophantine geometry.
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