Context: I recently chatted with a postdoc from russia, and we somehow got on the topic of learning mathematics and textbooks, and he told me about a wonderful textbook by Yuri Manin, on algebraic geometry which was written at the beginning of the seventies and wildely used for a long time in the former SU. He was so full of praise that I decided to check it out.

Now the problem I checked our library catalog and amazon.com and can't find anything that I can identify as this AG-textbook.

Question: So does this book exists? What's it's title? Was it maybe not translated?. Q2: If anyone has anything interesting to say about the book this would also be appreciated.

PS: I also speak german so if you know a german translation please also post.


3 Answers 3


Do you mean these:

Apparently the second is based on Théorie globale des intersections et théorème de Riemann-Roch SGA 6, Exp. 0.

Here are some djvu scans of the Russian versions:

  • $\begingroup$ Thanks I guess that's exactly the book/lecture notes. Does anyone know whether a translation exists? $\endgroup$
    – sisn
    Aug 4, 2011 at 17:18
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    $\begingroup$ Yes, at least for the second. I have a copy of "Lectures on the K-functor..." in English from Russian Math. Surveys vol 24, 1969. $\endgroup$ Aug 4, 2011 at 18:40
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    $\begingroup$ I have both, the affine schemes , but some Moscow people told me that there was another version which is bigger than affine schemes volume and has no intersection with K-theory chapters in UMN. I am not sure if this is true. $\endgroup$ Aug 4, 2011 at 20:25
  • $\begingroup$ thanks to both of you for your comments. @Thanks Donu this was really helpful, sadly the article is 60$, I will try to check if we have an institutional subscription. @Zoran This sounds interesting too, where did you get your's from? $\endgroup$
    – sisn
    Aug 4, 2011 at 21:40
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    $\begingroup$ @sisn: "K-functor..." from Russ. Math. Surv.: justpasha.org/math/links/files/manin/lectures-on-k-functor.djvu $\endgroup$ Aug 8, 2011 at 14:52

There now is a book by Manin Introduction to the theory of schemes (Translated from the Russian, edited and with a preface by Dimitry Leites) recently published by Springer based on Manin's lectures on algebraic geometry mentioned in David Roberts' post.


Hope this helps: Manin's lectures on algebraic geometry

Its the first part of Manin's 1966-1968 course (the one Zoran mentioned), chapters 1-26 . It's been scanned just recently.

  • $\begingroup$ The link given by Dmitry on the answer behind the link here is broken. $\endgroup$
    – David Roberts
    Apr 10, 2014 at 4:28

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