Algebraic Geometry - J.S. Milne Top

Group Theory

Fields and Galois Theory

Algebraic Geometry

Algebraic Number Theory

Modular Functions and Modular Forms

Elliptic Curves -- see books.

Abelian Varieties

Lectures on Etale Cohomology

Class Field Theory

Complex Multiplication

Basic Theory of Affine Group Schemes

Lie Algebras, Algebraic Groups, and Lie Groups

Reductive Groups

Errata

These notes are an introduction to the theory of algebraic varieties emphasizing the similarities to the theory of manifolds. In contrast to most such accounts they study abstract algebraic varieties, and not just subvarieties of affine and projective space. This approach leads more naturally into scheme theory.

- Preliminaries from commutative algebra
- Algebraic sets
- Affine algebraic varieties
- Local study
- Algebraic varieties
- Projective varieties
- Complete varieties
- Normal varieties; (Quasi-)finite maps; Zariski's main theorem
- Regular maps and their fibres Solutions to the Exercises

Index

Title | Date | Pages | |||
---|---|---|---|---|---|

10 | Algebraic schemes: geometry over an arbitrary field | ??? | pages | ||

11 | Surfaces (Intersection theory; Differentials; Riemann-Roch; Riemann hypothesis for curves) | ??? | pages | ||

12 | Divisors and intersection theory | 08.07.15 | 7 pages | ||

13 | Coherent sheaves; invertible sheaves | 08.07.15 | 7 pages | ||

14 | Differentials (Outline) | 08.07.15 | 2 pages | ||

15 | Algebraic varieties over the complex numbers | 08.07.15 | 3 pages | ||

16 | Descent theory | 09.07.15 | 20 pages | ||

17 | Lefschetz pencils | 09.07.15 | 3 pages | ||

18 | Schemes | ??? | pages | ||

19 | Cohomology | ??? | pages | ||

20 | The Riemann-Roch-Grothendieck theorem | ??? | pages | ||

A | Annotated Bibliography | 00.00.01 | 3 pages |

v3.01 (June 13, 1998). Added 5 sections (25 pages) and an index. Minor changes to Sections 0-8. 157pp.

v4.00 (October 30, 2003). Fixed errors; many minor revisions; added exercises; added two sections; 206 pages.

v5.00 (February 20, 2005). Heavily revised; most numbering changed; 227 pages. pdf (old version 5.00)

v5.10 (March 19, 2008). Minor fixes; TeX style changed, so page numbers changed; 241 pages.pdf (old version 5.10)

v5.20 (September 14, 2009). Minor corrections; revised Chapters 1,11,16; 245 pages. pdf (old version 5.20)

v5.21 (March 31, 2011). Minor changes; changed TeX style; 258 pages.

v5.22 (January 13, 2012). Minor fixes; 260 pages. pdf (old version 5.22)

v6.00 (August 24, 2014). Heavily revised. Split off the basic first course from the topics; 223+ pages.

v6.01 (August 23, 2015). Minor fixes; 226 pages.

v6.02 (March 19, 2017). Minor fixes; 221 pages.