by Andreas Gathmann
Publisher: University of Kaiserslautern 2014
Number of pages: 133
From the table of contents: Introduction; Affine varieties; Functions, morphisms, and varieties; Projective varieties; Dimension; Schemes; First applications of scheme theory; More about sheaves; Cohomology of sheaves; Intersection theory; Chern classes.
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by J. S. Milne
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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The author's aim has been to produce a book suitable to the beginner who wishes to acquire a sound knowledge of the more elementary parts of the subject, and also sufficient for the candidate for a mathematical scholarship.
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These notes are an enlarged version of a three-month course of lectures. Their style is informal. I hope they will serve as an introduction to some current research topics, for students who have had a one year course in modern algebraic geometry.
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