The Heart of Cohomology
|Rating||:||4.65 (788 Votes)|
|Number of Pages||:||191 Pages|
It is accordingly an idiosyncratic work, with a variety of human elements poking through the mathematics at nearly every corner. From the reviews:"This book teems with the author’s joy in his subject. … It can be recommended to anyone interested in a quick introduction to abstract cohomology theory.” (Ch. 154 (1), May, 2008). Baxa, Monatshefte für Mathematik, Vol. … Kato’s The Heart of Cohomology is a pleasure to read and it’ll be a pleasure to come back to it again and again." (Michael Berg, MathDL, December, 2007)“This monograph is an expanded version of the lecture notes for a short course titled ‘Introduction to Derived Categories’ given by the author at the University of Antwerp in 2004
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. If you have not heard about cohomology, The Heart of Cohomology may be suited for you. In addition, the book examines cohomological aspects of D-modules and of the computation of zeta functions of the Weierstrass family.
Suppresses author's personality, with dry result A. J. Sutter 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