Introduction to the Theory of Schemes

1. Front Matter

   Pages i-xvi

   PDF

2. Affine Schemes

   • Yuri I. Manin

   Pages 1-105

3. Sheaves, Schemes, and Projective Spaces

   • Yuri I. Manin

   Pages 107-193

4. Back Matter

   Pages 195-205

   PDF

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

• spectrum of a ring
• sheaf theory
• Manin
• algebraic geometry
• lecture notes

“This slim volume is still a valuable introduction to schemes and nicely complements the textbooks on this topic which have appeared in the meantime.” (C. Baxa, Monatshefte für Mathematik, Vol. 201 (4), August, 2023)

“Throughout the text there are many instructive examples, remarks, and clarifying footnotes. The style of exposition is rather concise, very elegant, extremely lucid and enlightening, versatile, and – despite its venerable age of fifty years – absolutely modern and timely. … an excellent source for students, instructors, and mathematical physicists. No doubt, with this textbook, the mathematical community has another general standard reference in algebraic geometry at its disposal.” (Werner Kleinert, zbMATH 1390.14002, 2018)

• Max Planck Institute for Mathematics , Bonn, Germany

  Yuri I. Manin

Yuri I. Manin is a retired scientific member of the Max Planck Institute for Mathematics in Bonn. He has received various prizes and notable awards, including the Moscow Mathematical Society Award (1963), the Lenin Prize (1967), the Brouwer Gold Medal (1987), the Frederic Esser Nemmers Prize (1994), the Rolf Schock Prize (1999), the King Faisal Prize for Mathematics, the Georg Cantor Medal of the German Mathematical Society (2002) and the Bolyai Prize (2010).

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