Timeline for textbooks on modern algebraic geometry for 21st-century starters
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 23, 2014 at 23:18 | comment | added | bananastack | @DavidSpeyer: thanks. That's actually the book where I first learned homological algebra and loved it. Although there are a lot of topics there in the algebro-geometric side, I was hoping to expand my knowledge in the algebro-topological. | |
| Dec 19, 2014 at 2:11 | comment | added | David E Speyer | @bananastack If I understand what you are looking for, <i>Methods of Homological Algebra</i> by Gelfand and Manin fits the bill. Beware the many minor typos. | |
| Dec 16, 2014 at 0:46 | comment | added | user62675 | @W.Z. Imagine trying to read Lurie's Higher Algebra without first understanding what $\infty$-categories actually are and what they could be used for. It's not a good idea to rush through the basics in order to reach some great goal, like AG from stacks, but that final goal should/could be something to keep in mind when reading, so you know what you'll be up against once you reach that point. | |
| Dec 16, 2014 at 0:35 | comment | added | user62675 | @user125763 Of course, I agree with you on starting to learn AG from either source, but I don't think we want flame wars either (I don't know who the user is, though)! :-) RE your next comment - I'm not an expert, simply a beginner, but I don't recall any book that studies homological algebra from the derived context. I'm sure there's something out there, though! | |
| Dec 16, 2014 at 0:34 | comment | added | bananastack | @RingSpectra: actually, I'd like to ask you a question, since you seem to know a fair bit of derived technology. Do you know of any book on homological algebra which uses the derived point of view? For example discussing cup products via Ext and maybe results like in this blog post? amathew.wordpress.com/2012/05/15/… | |
| Dec 16, 2014 at 0:34 | comment | added | W.Z. | @Ring Spectra Thank you for your generous answer with links. Could you also please comment a little bit more on your last parenthesized statement? I am just curious. | |
| Dec 16, 2014 at 0:32 | comment | added | bananastack | I don't think anyone should start learning algebraic geometry from either source. Certainly, after spending a fair amount of time over Eisenbud-Harris, Hartshorne and friends, I profited immensely from Toën's notes when trying to understand the basics of stacks (I just think that the functorial point of view makes things more transparent). After that, Lurie's thesis (or at least the small part I actually read) was just a very pleasant read. We already had a famous MO user who thought she should do away with classical AG, I don't think we need to rekindle the flame wars. | |
| Dec 16, 2014 at 0:27 | comment | added | user62675 | @user125763 That's true. Lurie's thesis is on derived algebraic geometry, though, and I don't really think that the OP should read that unless he/she has a firm grip of algebraic geometry and knows (some) algebraic topology, like homotopy theory. | |
| Dec 16, 2014 at 0:21 | comment | added | bananastack | I think for what the OP is asking, Toën's notes are unbeatable (at least for a first introduction to the language). After that you might as well pick up Lurie's thesis. dspace.mit.edu/handle/1721.1/30144 | |
| S Dec 15, 2014 at 23:52 | history | answered | user62675 | CC BY-SA 3.0 | |
| S Dec 15, 2014 at 23:52 | history | made wiki | Post Made Community Wiki by user62675 |