Lectures on Deformations of Singularities
by Michael Artin
Publisher: Tata Institute of Fundamental Research 1976
Number of pages: 110
These notes are based on a series of lectures given at the Tata Institute in January-February, 1973. The lectures are centered about the work of M. Scahlessinger and R. Elkik on infinitesimal deformations. Contents: Formal Theory and Computations; Elkik's Theorems on Algebraization.
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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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These notes develop the theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. It assumed that the reader is familiar with some basic properties of rings, ideals, and polynomials.
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