Timeline for textbooks on modern algebraic geometry for 21st-century starters
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 14, 2016 at 17:48 | answer | added | loift | timeline score: 1 | |
| Dec 19, 2014 at 16:39 | comment | added | user1437 | I like the general spirit of this question even if it doesn't have a good answer. There are many applications of algebraic geometry to pure algebra and representation theory that require certain machinery not well elucidated in books like Hartshorne's or Liu's (derived categories are an example). For people more interested in these applications instead of pure algebraic geometry, the "classic texts" are very unmotivated. | |
| Dec 19, 2014 at 1:05 | comment | added | Daniel Barter | I disagree with your comment about higher sheaves not being motivated well. As soon as you start talking about functor of points and moduli problems, stacks / groupoid valued functors pop up pretty fast | |
| Dec 18, 2014 at 23:50 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Dec 18, 2014 at 23:19 | history | edited | Ricardo Andrade |
replaced tag 'reference-request' with tag 'textbook-recommendation'
|
|
| Dec 16, 2014 at 22:43 | comment | added | user62675 | @Jon I couldn't agree more with you! (I think this is reflected in the last paragraph of my answer below.) | |
| Dec 16, 2014 at 4:06 | comment | added | user74230 | @W.Z.: I don't wish to get into an extended discussion about this; please just follow my advice to talk in person with a professional algebraic geometer. If the goal is to actually understand things in a serious way and to become a creative user of these ideas then what you have in mind is a very very bad idea. I have nothing more to say. | |
| Dec 16, 2014 at 1:12 | comment | added | Jonathan Beardsley | I might add that without a good understanding of homological algebra, really important concepts like sheaf cohomology and derived functors aren't going to make much sense. For that, I strongly recommend Charles Weibel's book. It's encyclopedic and well written. The only drawback is that some of his terminology is non-standard. | |
| Dec 16, 2014 at 1:09 | comment | added | Jonathan Beardsley | Ultimately, it really really really depends on what you want to do. You may be the sort of person who can just start memorizing a lot of terminology and abstract nonsense, but if you have no intuition for what a scheme is, you're unlikely to be able to prove very much about schemes. On the other hand, I came from topology, and it was very useful for me to be able to just thing about a stack from the category theory perspective. So it might be worth it to provide some context in your question. | |
| Dec 15, 2014 at 23:52 | answer | added | user62675 | timeline score: 5 | |
| Dec 15, 2014 at 23:29 | comment | added | Ashwath Rabindranath | Just my opinion (and I am not an expert in these modern homological ideas) but I think that there's a real risk in learning these ideas without first going through the grind of learning classical algebraic geometry and Hartshorne-type material (I guess today Hartshorne is classical algebraic geometry too!). Of course if you have already mastered Hartshorne, this comment does not apply. | |
| Dec 15, 2014 at 22:52 | comment | added | W.Z. | @jmc Stacks Project is not a textbook. | |
| Dec 15, 2014 at 22:48 | comment | added | W.Z. | @user74230 I just want everything to be conceptually concise at as early stage as possible. To get a real feel of how machinery works, it consumes time, so choosing the more advanced concepts to mess with might be saving time since the earlier students get exposed to them the better as soon as a proper introduction is provided. It's just my own thought. | |
| Dec 15, 2014 at 22:11 | comment | added | user74230 | You should talk to some professional algebraic geometers, as (IMHO) your perception of how one should go about learning the subject is misguided. The idea that derived categories and stacks should be included as part of an introduction to algebraic geometry is badly mistaken. It is like advocating that introductory physics should include General Relativity and quantum mechanics, since those are more or less standard in many aspects of physics at the professional level. The challenges of education are serious. | |
| Dec 15, 2014 at 20:55 | comment | added | prefaisceau | See the related question : mathoverflow.net/questions/12765/algebraic-stacks-from-scratch | |
| S Dec 15, 2014 at 20:33 | history | suggested | Tadashi |
Added relevant tag
|
|
| Dec 15, 2014 at 20:24 | review | Suggested edits | |||
| S Dec 15, 2014 at 20:33 | |||||
| Dec 15, 2014 at 18:44 | comment | added | jmc | I assume you know of stacks.math.columbia.edu? | |
| Dec 15, 2014 at 18:41 | history | asked | W.Z. | CC BY-SA 3.0 |