By Kenji Ueno
This can be a reliable ebook on very important principles. however it competes with Hartshorne ALGEBRAIC GEOMETRY and that's a tricky problem. It has approximately a similar must haves as Hartshorne and covers a lot a similar rules. the 3 volumes jointly are literally a section longer than Hartshorne. I had was hoping this might be a lighter, extra simply surveyable booklet than Hartshorne's. the topic consists of an immense volume of fabric, an total survey displaying how the elements healthy jointly may be very necessary, and the IWANAMI sequence has a few superb, short, effortless to learn, overviews of such subjects--which supply evidence thoughts yet refer somewhere else for the main points of a few longer proofs. however it seems that Ueno differs from Hartshorne within the different path: He provides extra specific nuts and bolts of the elemental buildings. total it really is more uncomplicated to get an summary from Hartshorne. Ueno does additionally supply loads of "insider details" on the right way to examine issues. it's a reliable publication. The annotated bibliography is particularly attention-grabbing. yet i need to say Hartshorne is better.If you get caught on an workout in Hartshorne this booklet will help. when you are operating via Hartshorne by yourself, you'll find this replacement exposition worthwhile as a better half. you may just like the extra vast hassle-free therapy of representable functors, or sheaves, or Abelian categories--but you'll get these from references in Hartshorne as well.Someday a few textbook will supercede Hartshorne. Even Rome fell after adequate centuries. yet here's my prediction, for what it really is worthy: That successor textbook usually are not extra basic than Hartshorne. it is going to benefit from growth for the reason that Hartshorne wrote (almost 30 years in the past now) to make a similar fabric faster and easier. it is going to comprise quantity concept examples and may deal with coherent cohomology as a distinct case of etale cohomology---as Hartshorne himself does in brief in his appendices. will probably be written via an individual who has mastered each point of the math and exposition of Hartshorne's e-book and of Milne's ETALE COHOMOLOGY, and prefer either one of these books it is going to draw seriously on Grothendieck's significant, unique, yet thorny components de Geometrie Algebrique. after all a few humans have that point of mastery, particularly Deligne, Hartshorne, and Milne who've all written nice exposition. yet they cannot do every little thing and not anyone has but boiled this right down to a textbook successor to Hartshorne. for those who write this successor *please* permit me understand as i'm loss of life to learn it.
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Additional resources for Algebraic Geometry 2: Sheaves and Cohomology (Translations of Mathematical Monographs) (Vol 2)
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