Like many graduate students before trying to learn something about étale cohomology and Deligne's proof(s) of the Riemann hypothesis part of the Weil conjectures, I am hunting for references detailing basic sheaf-theoretic operations in the classical topology.

Here are some sources I found so far which discuss this, some of which by way of wise words of Bhargav Bhatt and Matt Emerton somewhere online.

  • Freitag and Kiehl's book on étale cohomology and the Weil conjectures.
  • Milne's book on étale cohomology.
  • Kashiwara and Schapira's book on sheaves on manifolds.
  • Borel's book on intersection cohomology.
  • Last but not least, notes from Conrad's seminar on Deligne-Laumon. http://math.stanford.edu/~conrad/Weil2seminar/

But there's gotta be more! Specifically, I would appreciate pointers towards perhaps some sources penned by some more recent and younger "masters" -- although notes from Conrad's seminar pretty much fit this bill. But really, just suggest your favorite source that hasn't been listed yet, and perhaps give a reasoning what value it has over the ones I have listed already.

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    $\begingroup$ I can't tell what your background is, but I'm not sure I would recommend starting with any of the above for what you seem to want. Chapters II and III of Hartshorne's AG is not a bad introduction to sheaf theory. There are also several books on sheaf theory/cohomology in English, I really like one by Iverson. If you read French, Godement's Theorie des faisceaux is arguably the best reference. $\endgroup$ Oct 7, 2017 at 13:09
  • $\begingroup$ I second Arapura's recommendations, especially (Part II of) Godement's masterpiece. (Also, learn to read mathematical French if you have interests in this kind of math; that involves less language skill than reading a French menu.) That classic reference remains a fantastic resource. Sources from long ago (such as in Seminaire Cartan on various topics, to say nothing of EGA, Bourbaki exposes, etc.) can retain their vitality and relevance over anything written by "more recent and younger" people. Also see Ch. 5 in Frank Warner's book Foundations of... and Iversen's Cohomology of sheaves. $\endgroup$
    – nfdc23
    Oct 7, 2017 at 13:35
  • $\begingroup$ Dimca's "Sheaves in Topology" seems to fit the bill. It is like an easier version of Kashiwara and Schapira. $\endgroup$ Oct 7, 2017 at 13:49


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