This course provides an introduction to the language of schemes,
properties of morphisms, and sheaf cohomology. Covered topics are: Basics of
category theory, Sheaves, Abelian sheaves, Schemes, Morphisms of schemes,
Sheaves of modules, More properties of morphisms, Projective morphisms,
Projective morphisms, Flat morphisms and descent, Differentials Divisors,
Divisors on curves, Homological algebra, Sheaf cohomology, Cohomology of
quasicoherent sheaves, Cohomology of projective spaces, Hilbert polynomials,
GAGA, Serre duality for projective space, Dualizing sheaves and RiemannRoch,
CohenMacaulay schemes and Serre duality, Higher RiemannRoch and Etale
cohomology.
This book is intended to give a
serious and reasonably complete introduction to algebraic geometry, not just for
experts in the field. Topics covered includes: Sheaves, Schemes, Morphisms of
schemes, Useful classes of morphisms of schemes, Closed embeddings and related
notions, Fibered products of schemes, and base change, Geometric properties:
Dimension and smoothness, Quasicoherent sheaves, Quasicoherent sheaves on
projective A-schemes, Differentials,Derived functors, Power series and the
Theorem on Formal Functions, Proof of Serre duality.
This note contains the following subtopics of Algebraic Geometry,
Theory of Equations, Analytic Geometry, Affine Varieties and Hilbert’s
Nullstellensatz , Projective Varieties and Bezout’s Theorem, Epilogue
This course provides an introduction to the language of schemes,
properties of morphisms, and sheaf cohomology. Covered topics are: Basics of
category theory, Sheaves, Abelian sheaves, Schemes, Morphisms of schemes,
Sheaves of modules, More properties of morphisms, Projective morphisms,
Projective morphisms, Flat morphisms and descent, Differentials Divisors,
Divisors on curves, Homological algebra, Sheaf cohomology, Cohomology of
quasicoherent sheaves, Cohomology of projective spaces, Hilbert polynomials,
GAGA, Serre duality for projective space, Dualizing sheaves and RiemannRoch,
CohenMacaulay schemes and Serre duality, Higher RiemannRoch and Etale
cohomology.
This note covers the
following topics: The Pre-cursor of Bezout’s Theorem: High School Algebra, The
Projective Plane and Homogenization, Bezout’s Theorem and Some Examples.
Author(s): Stephanie
Fitchett, Florida Atlantic University Honors College
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.
This book covers the following topics:
Elementary Algebraic Geometry, Dimension, Local Theory, Projective Geometry,
Affine Schemes and Schemes in General, Tangent and Normal Bundles, Cohomology,
Proper Schemes and Morphisms, Sheaves and Ringed Spaces.