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Yuriy Drozd Intriduction to Algebraic Geometry

This note explains the following topics: Affine Varieties, Hilbert�s Nullstell, Projective and Abstract Varieties, Grassmann varieties and vector bundles, Finite morphisms, Dimension Theory, Regular and singular points, Tangent space, Complete local rings, Intersection theory.

Author(s): Yuriy Drozd

104 Pages

This PDF book covers the following topics related to Algebraic Geometry : General Remarks on Computer Algebra Systems, The Geometry�Algebra Dictionary, Affine Algebraic Geometry, Ideals in Polynomial Rings, Affine Algebraic Sets, Hilbert�s Nullstellensatz, Irreducible Algebraic Sets, Removing Algebraic Sets, Polynomial Maps, The Geometry of Elimination, Noether Normalization and Dimension, Local Studies, Projective Algebraic Geometry, The Projective Space, Projective Algebraic Sets, Affine Charts and the Projective Closure, The Hilbert Polynomial, Computing, Standard Bases and Singular, Applications, Ideal Membership, Elimination, Radical Membership, Ideal Intersections, Ideal Quotients, Kernel of a Ring Map, Integrality Criterion, Noether Normalization, Subalgebra Membership, Homogenization, Dimension and the Hilbert Function, Primary Decomposition and Radicals, Buchberger�s Algorithm and Field Extensions, Sudoku, A Problem in Group Theory Solved by Computer Algebra, Finite Groups and Thompson�s Theorem, Characterization of Finite Solvable Groups.

Author(s): Wolfram Decker, Gerhard Pfister

133 Pages

Lectures notes in universal algebraic geometry Artem N. Shevlyakov

The contents of this book include: Introduction, Algebraic structures, Subalgebras, direct products, homomorphisms, Equations and solutions, Algebraic sets and radicals, Equationally Noetherian algebras, Coordinate algebras, Main problems of universal algebraic geometry, Properties of coordinate algebras, Coordinate algebras of irreducible algebraic sets, When all algebraic sets are irreducible, The intervention of model theory, Geometrical equivalence, Unifying theorems, Appearances of constants, Coordinate algebras with constants, Equational domains, Types of equational compactness, Advances of algebraic geometry and further reading.

Author(s): Artem N. Shevlyakov

67 Pages

Introduction to Algebraic Geometry by Igor V. Dolgachev

This book explains the following topics: Systems of algebraic equations, Affine algebraic sets, Morphisms of affine algebraic varieties, Irreducible algebraic sets and rational functions, Projective algebraic varieties, Morphisms of projective algebraic varieties, Quasi-projective algebraic sets, The image of a projective algebraic set, Finite regular maps, Dimension, Lines on hypersurfaces, Tangent space, Local parameters, Projective embeddings and Riemann-Roch Theorem.

Author(s): Igor V. Dolgachev

198 Pages

Lectures on Etale Cohomology

This book explains the following topics: Etale Morphisms, Etale Fundamental Group, The Local Ring for the Etale Topology, Sheaves for the Etale Topology, Direct and Inverse Images of Sheaves, Cohomology: Definition and the Basic Properties, Cohomology of Curves, Cohomological Dimension, Purity; the Gysin Sequence, The Proper Base Change Theorem, Cohomology Groups with Compact Support, The Smooth Base Change Theorem, The Comparison Theorem, The Kunneth Formula, Proof of the Weil Conjectures, The Weil Conjectures, The Geometry of Lefschetz Pencils and Cohomology of Lefschetz Pencils.

Author(s): J.S. Milne

202 Pages

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Yuriy Drozd Intriduction to Algebraic Geometry

Yuriy Drozd Intriduction to Algebraic Geometry

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