Computations in Algebraic Geometry with Macaulay 2
by D. Eisenbud, D. Grayson, M. Stillman, B. Sturmfels
Publisher: Springer 2001
Number of pages: 343
This book presents algorithmic tools for algebraic geometry and experimental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications.
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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.
by Ralph Howard - Royal Institute of Technology Stockholm
The main goal of these notes is to give a proof of the basic facts of harmonic analysis on compact symmetric spaces and then to apply these to concrete problems involving things such as the Radon and related transforms on these spaces.
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These notes are an introduction to the theory of algebraic varieties. In contrast to most such accounts they study abstract algebraic varieties, not just subvarieties of affine and projective space. This approach leads naturally to scheme theory.
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The book covers linear algebraic groups and arithmetic groups, adeles and arithmetic properties of algebraic groups, automorphic functions and spectral decomposition of L2-spaces, vector valued cohomology and deformation of discrete subgroups, etc.