Introduction to the Theory of Schemes

verfasst von: Yuri I. Manin

Verlag: Springer International Publishing

Buchreihe : Moscow Lectures

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Einloggen, um Zugang zu erhalten

Über dieses Buch

This English edition of Yuri I. Manin's well-received lecture notes provides a concise but extremely lucid exposition of the basics of algebraic geometry and sheaf theory. The lectures were originally held in Moscow in the late 1960s, and the corresponding preprints were widely circulated among Russian mathematicians.
This book will be of interest to students majoring in algebraic geometry and theoretical physics (high energy physics, solid body, astrophysics) as well as to researchers and scholars in these areas.
"This is an excellent introduction to the basics of Grothendieck's theory of schemes; the very best first reading about the subject that I am aware of. I would heartily recommend every grad student who wants to study algebraic geometry to read it prior to reading more advanced textbooks."- Alexander Beilinson

Inhaltsverzeichnis

Frontmatter

Chapter 1. Affine Schemes

Abstract

Studying algebraic equations is an ancient aspect of the mathematical science. In modern times, vogue and convenience dictate us to turn to rings.

Yuri I. Manin

Chapter 2. Sheaves, Schemes, and Projective Spaces

Abstract

The topological space Spec A is by itself a rather coarse invariant of A, see Examples 1.5.3. Therefore, as the “right” geometric object corresponding to A, it is natural to take the pair (Spec A, Ã) consisting of the space Spec A and the set of elements of A considered, more or less adequately, as functions on Spec A, and so we did up to now.

Yuri I. Manin

Backmatter

Titel: Introduction to the Theory of Schemes
verfasst von: Yuri I. Manin
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-74316-5
Print ISBN: 978-3-319-74315-8
DOI: https://doi.org/10.1007/978-3-319-74316-5