by Winfried Bruns, Udo Vetter
Publisher: Springer 1988
Number of pages: 244
Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. Their study has attracted many prominent researchers and has motivated the creation of theories which may now be considered part of general commutative ring theory. The book gives a first coherent treatment of the structure of determinantal rings. The main approach is via the theory of algebras with straightening law.
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by Armand Borel, George D. Mostow - American Mathematical Society
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.
by Alexander Kleshchev - University of Oregon
Contents: General Algebra; Commutative Algebra; Affine and Projective Algebraic Sets; Varieties; Morphisms; Tangent spaces; Complete Varieties; Basic Concepts; Lie algebra of an algebraic group; Quotients; Semisimple and unipotent elements; etc.
by Sudhir R. Ghorpade - Indian Institute of Technology Bombay
This text is a brief introduction to algebraic geometry. We will focus mainly on two basic results in algebraic geometry, known as Bezout's Theorem and Hilbert's Nullstellensatz, as generalizations of the Fundamental Theorem of Algebra.
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.