Lectures on Logarithmic Algebraic Geometry
by Arthur Ogus
Publisher: University of California, Berkeley 2006
Number of pages: 255
Logarithmic geometry was developed to deal with two fundamental and related problems in algebraic geometry: compactification and degeneration. Contents: The geometry of monoids; Log structures and charts; Morphisms of log schemes; Differentials and smoothness; De Rham and Betti cohomology.
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by P. Samuel - Tata Institute Of Fundamental Research
The aim of this text is to give a proof, due to Hans Grauert, of an analogue of Mordell's conjecture. Contents: Introduction; Algebro-Geometric Background; Algebraic Curves; The Theorem of Grauert (Mordell's conjecture for function fields).
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Introduction to both the geometry and the arithmetic of abelian varieties. It includes a discussion of the theorems of Honda and Tate concerning abelian varieties over finite fields and the paper of Faltings in which he proves Mordell's Conjecture.
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This is an introduction to the arithmetic theory of modular functions and modular forms, with an emphasis on the geometry. Prerequisites are the algebra and complex analysis usually covered in advanced undergraduate or first-year graduate courses.