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 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).
by H. Maass - Tata Institute of Fundamental Research
Contents: Modular Group of Degree n; Symplectic group of degree n; Reduction Theory of Positive Definite Quadratic Forms; Fundamental Domain of the Modular Group of Degree n; Modular Forms of Degree n; Algebraic dependence of modular forms; etc.
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This text is a motivational survey of geometric algebra in 3D. The intention here was to use simple examples and reader is referred to the independent problem solving. The active reading of text is recommended, with paper and pencil in hand.
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.