# Solutions to Hartshorne's Algebraic Geometry

The goal of this book is to eventually provide a complete, correct, central set of solutions to the exercises in Hartshorne's graduate textbook "Algebraic Geometry". There are many exercises which appear in EGA and a secondary goal would be to have references to all of these.

This project is very, very young but should grow quickly as latex solutions for many exercises (see below) are available and just need to be transferred here. If you want to help with this process mention it on the discussion page (link top left).

## Solutions which appear in this wikibookEdit

• II.1 Sheaves:
• II.2 Schemes:
• II.3 First Properties of Schemes:
• II.4 Separated and Proper Morphisms: 1, 2, 3, 4.
• II.5 Sheaves of Modules:
• II.6 Divisors:
• II.7 Projective Morphisms:
• II.8 Differentials:
• III.2 Cohomology of Sheaves:
• III.3 Cohomology of a Noetherian Affine Scheme:
• III.4 Cech Cohomology:
• III.5 The Cohomology of Projective Space:
• III.6 Ext Groups and Sheaves:
• III.7 The Serre Duality Theorem:
• III.8 Higher Direct Images of Sheaves:
• III.9 Flat Morphisms:

## Solutions which don't appear yet in this wikibookEdit

• All of Chapter I
• II.1 Sheaves: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22.
• II.2 Schemes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.
• II.3 First Properties of Schemes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23.
• II.4 Separated and Proper Morphisms: 5, 6, 8, 9, 10, 11, 12.
• II.5 Sheaves of Modules: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.
• II.6 Divisors: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
• II.7 Projective Morphisms: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.
• II.8 Differentials: 1, 2, 3, 4, 5, 6, 7, 8.
• II.9 Formal Schemes: 1, 2, 3, 4, 5, 6.
• All of Chapter III
• All of Chapter IV
• All of Chapter V

## Solutions to be transferred here for which latex code is availableEdit

• II.1 Sheaves: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22.
• II.2 Schemes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19.
• II.3 First Properties of Schemes: 1, 2, 3, 4, 5, 6, 7, 9, 10, 13, 14, 16, 17, 18.
• II.4 Seperated and Proper Morphisms: 1, 2, 3, 4, 6, 8, 9.
• II.5 Sheaves of Modules: 2, 3, 4, 5, 6, 7, 8, 9, 10, 14, 15, 16.
• II.6 Divisors: 1, 4, 11.
• II.7 Projective Morphisms: 1, 2, 4, 5, 6, 7, 8, 9, 12.
• II.8 Differentials: 1, 2, 3, 5, 6, 7, 8.
• III.2 Cohomology of Sheaves: 2, 3, 4, 5, 6.
• III.3 Cohomology of a Noetherian Affine Scheme: 1, 2, 3, 5, 7, 8.
• III.4 Cech Cohomology: 1, 3, 5, 6, 7, 9, 11.
• III.5 The Cohomology of Projective Space: 1, 4, 10.
• III.6 Ext Groups and Sheaves: 1, 3, 4, 5, 6, 7, 8, 9.
• III.7 The Serre Duality Theorem: 3.
• III.8 Higher Direct Images of Sheaves: 1, 2, 3.
• III.9 Flat Morphisms: 1, 2, 7, 9.