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.
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by Pierre Schapira - UPMC
The aim of these lecture notes is first to introduce the reader to the theory of D-modules in the analytical setting and also to make a link with the theory of deformation quantization (DQ for short) in the complex setting.
by Donu Arapura - Purdue University
Algebraic geometry is the geometric study of sets of solutions to polynomial equations over a field (or ring). In this book the author maintains a reasonable balance between rigor and intuition; so it retains the informal quality of lecture notes.
by Claude Sabbah - arXiv
The purpose of these lectures is to introduce the notion of a Stokes-perverse sheaf as a receptacle for the Riemann-Hilbert correspondence for holonomic D-modules. They develop the original idea of P. Deligne in dimension one.
by Yuriy Drozd
From the table of contents: Affine Varieties; Ideals and varieties. Hilbert's Basis Theorem. Regular functions and regular mappings. Projective and Abstract Varieties; Dimension Theory; Regular and singular points; Intersection theory.