The Heart of Cohomology 2006th Edition by Goro Kato (PDF)

Description

If you have not heard about cohomology, The Heart of Cohomology may be suited for you. The book gives Fundamental notions in cohomology for examples, functors, representable functors, Yoneda embedding, derived functors, spectral sequences, derived categories are explained in elementary fashion. Applications to sheaf cohomology. In addition, the book examines cohomological aspects of D-modules and of the computation of zeta functions of the Weierstrass family.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This isn’t a review in the usual sense, since maybe its ideal reader is the book’s author, rather than prospective purchasers. But if, by chance, you’re familiar with the Japanese book of the same title by the same author (Iwanami Shouten 2003), the Springer edition will be a disappointment. The Japanese version is written in a conversational style, with more diagrams than appear to be in the Springer edition (including some diagrams of mountains, picture frames, etc.) and fanciful terms like “abstract nonsense,” “general nonsense,” “flabby sheaf,” “the Trinity,” etc.By comparison, the Springer edition is much more formal and dry. E.g., instead of an anecdote about Saul Lubkin (Japanese ed. @ 27), you’ll get a citation to one of his papers (English ed. @ 17). The style isn’t as austere as definition-theorem-proof, but comes close, with sentences much more symbol-heavy than in the original. The organization of the chapters is also quite different. Had I discovered this version first, I would have put it back on the shelf.This isn’t a matter of a bad translator; according to the preface, Prof. Goto seems to have prepared the English manuscript himself. So the stylistic difference apparently is based on his impression of how “gaijin” (non-Japanese) like their math. I hope he will be brave enough to show more of his personality in his next book for the English-language market.

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