by J. S. Milne
Number of pages: 172
An introduction to both the geometry and the arithmetic of abelian varieties. It includes a discussion of the theorems of Honda and Tate concerning abelian varieties over finite fields and the paper of Faltings in which he proves Mordell's Conjecture.
Home page url
Download or read it online for free here:
by Lucia Caporaso, et al. - Cambridge University Press
An introductory panorama of current progress in the field, addressed to both beginners and experts. This volume offers expository overviews of the state of the art in many areas of algebraic geometry. Prerequisites are kept to a minimum ...
by Johan de Jong, et al.
The stacks project aims to build up enough basic algebraic geometry as foundations for algebraic stacks. This implies a good deal of theory on commutative algebra, schemes, varieties, algebraic spaces, has to be developed en route.
by Kiran S. Kedlaya
This is not a typical math textbook, it does not present full developments of key theorems, but it leaves strategic gaps in the text for the reader to fill in. The original text underlying this book was a set of notes for the Math Olympiad Program.
by Eckart Viehweg - Springer
This book discusses two subjects of quite different nature: Construction methods for quotients of quasi-projective schemes by group actions or by equivalence relations and properties of direct images of certain sheaves under smooth morphisms.