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There are a number of mathematical books/monographs that do not have indices. In some cases, this is no huge deal; for instance, it is often easy to find something in Bourbaki using the table of contents. However, sometimes it can be incredibly frustrating. For instance, in Mumford's Red Book, if you want to know what it means for a prescheme to be a scheme (in more recent terminology, what it means for a scheme to be separated), you have to look in the section titled "The functor of points of a prescheme." Pedagogically, it works, but who would ever think to look there?

Thus, my "question" has two parts:

1) Are there any good resources (online or otherwise) that provide indices for such works as the Red Book?
2) Assuming the answer to 1) is no, could we, as an online community, produce such a resource in the answers to this question (which I am making a community wiki for this purpose)?

To try to jumpstart 2), in case the answer to 1) is no, I am including as an answer a partial index I have produced for the Red Book. This is also to show I am not asking others to contribute to something that I myself have not put time into.

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If we end up doing 2), and someone knows of a better place for it, please suggest it. In any case, I am aware that this is a somewhat experimental question and may get closed. –  Charles Staats Jun 10 '10 at 4:29
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This is not quite what you're asking, but google books is very helpful here, since it has serchable copies of many indexless books. –  jeremy Jun 10 '10 at 4:36

3 Answers 3

Partial Index for Mumford's Red Book
[Note: page numbers followed by N indicate pages in the new edition, infamous for its typos.]

Associated point: III.2 (p. 147N)

Blow-up: III.3 (p. 159N)

Chow's Lemma: I.10 (p. 60N)

Examples: I: II: III: A, p. 142N; E, p. 155N; F bis, p. 164N; G, p. 171N; H, p. 185N; J, p. 195N; K, p. 199N; L, p. 202N; M, p. 207N; N, p. 208N; O, p. 211N; P, p. 217N

Hensel's Lemma: III.5 (p. 177N)

Geometric fibres: III.5 (p. 176N)

Jacobian criterion: III.6 (p. 185N)

Kahler differentials: III.1 (p. 142N)

Nagata Lemma: III.8 (p. 196N)
Nakayama's Lemma (geometric versions):III.2 (p. 152N)
Noether Normalization Lemma: I.1 (p. 2N)
-geometric form: I.7 (p. 42N)
-over ring R: II.8 (p. 129N)

Scheme (separated): II.6 (p. 118N)
Segre map: I.6 (p. 36N)
-Note: In III.8 (p. 203N), the Veronese map is incorrectly called the Segre map.

Veronese map: III.8 (p. 203N)
-cf. "Segre map"

$\Omega_{X/k}(x)$: cotangent space at $x$, III.4 (p. 169N)

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Mumford's "Red Book" is not really a book or monograph in the usual sense but started life as mimeographed lecture notes (bound with red paper covers). The later photographic reproduction as Springer Lecture Notes 1358 doesn't change the format or add indexing. This is still a useful resource, but isn't as reader-friendly as some of the more recent textbooks on algebraic geometry. It's always a useful educational exercise for an individual to add index entries or notes to such a volume, though even a careful group indexing effort would still be invisible to future readers if they didn't suspect its existence.

Other widely used lecture notes pose similar problems. For example, Steinberg's often-cited 1967-68 lectures on Chevalley groups at Yale have rich content in spite of some rough spots in the write-up but exist only in cumbersome versions with no index and no page headings for easy location of material. (Publishers like AMS have tried unsuccessfully to extract a more durable version.)

As noted, a few actual books lack indexes of any kind. An example is the otherwise valuable Birkhauser monograph Complex Geometry and Representation Theory by Chriss and Ginzburg, which I believe still lacks an index. But the individual chapters or multi-chapters of Bourbaki I own (in several of their "books") do have an "index des notations" (in order of appearance), an "index terminologique" (alphabetical), and finally a table of contents.

Much more commonly, advanced books often have incomplete or erratic indexes, partly due to older technology and reliance on authors to make up their own lists after the fact. More elementary textbooks or books written for a general audience tend to be indexed by professionals, one of whom is a sibling of mine and has lots to say about the fine points. Current software makes it much easier for authors to add index entries as they go along, but even so there is wide scope for individual judgment about inclusion/exclusion or how elaborate an index to construct. Aside from that, I prefer books to have a full table of contents, descriptive section headings, logical internal numbering, and page headers that make it easy to find your way around. But as I pointed out, the "Red Book" is not really a "book".

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One could consider looking for a text-searchable format on Gigapedia (for instance, the second edition of the Red Book is available in djvu). Is there a better way to search than text-searching in an ecopy? Not to my knowledge.

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Oftentimes, the OCR is quite bad. –  Harry Gindi Jun 10 '10 at 5:36
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I try not to use electronic resources of questionable legality. –  Charles Staats Jun 10 '10 at 13:37
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If you own the book, then you have the right to download any electronic copy you want. –  Harry Gindi Jun 11 '10 at 9:45
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Gigapedia does not exist. Please do not rock the boat. –  Anweshi Jul 26 '10 at 18:42

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