Лёня Посицельский (posic) wrote,
Лёня Посицельский


Since its inception around 1960, there has been very little literature on the theory of derived categories. In some respect, the only detailed account for many years was the original book [RD], written by Hartshorne following notes by Grothendieck. Several accounts appeared later as parts of the books [We], [GeMa], [KaSc1], [KaSc2], [Huy], and maybe a few others – but none of these accounts provided enough detailed content to make it possible for a mathematician to learn how to work with derived categories, beyond a rather superficial level. The theory thus remained mysterious.

A personal belief of mine is that mathematics should not be mysterious. Some mathematics is very easy to explain. However, a few branches of mathematics are truly hard; among them are algebraic geometry and derived categories. My moral goal in this book is to demonstrate that the theory of derived categories is difficult, but not mysterious.

The [EGA] series by Grothendieck and Dieudonné, and then the book [Har] by Hartshorne, have shown us that algebraic geometry is difficult but not mysterious. The definitions and the statements are precise, and the proofs are available (to be read or to be taken on trust, as the reader prefers). I hope that the present book will do the same for derived categories. (Although I doubt I can match the excellent writing talent of the aforementioned authors!)

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