Timeline for answer to Derived algebraic geometry: how to reach research level math? by Yonatan Harpaz
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| Sep 14, 2015 at 23:53 | comment | added | user40276 | @010110111 You may refer to the other chapters when necessary. However if you want to get the big picture, 1, 5 and 6 seems enough. After this it's possible to get a good idea of what's an $(\infty, 1)$-stack. Then (if you already have some background in moduli and some intersection theory) you can read the series of Töen and Vezzosi's papers about Homotopical Algebraic Geometry in arxiv and arxiv.org/abs/1401.1044 for the motivations (to use derived $(\infty, 1)$ Artin stacks). Together with these ones you can try Lurie's thesis (however it has few proofs). | |
| Sep 14, 2015 at 23:11 | comment | added | 010110111 | What about ch 2 of HTT? that also looks important. | |
| Sep 14, 2015 at 18:12 | comment | added | user40276 | Well, I don't think the entire HTT is strictly necessary. The chapters 1, 5 and 6 seems enough. | |
| Sep 14, 2015 at 6:58 | comment | added | Yonatan Harpaz | I agree, HTT is just a good place to start. After that one should delve into a more specific topic. For DAG which is based on spectra, Higher Algebra is undoubtedly the next step. | |
| Sep 13, 2015 at 23:36 | comment | added | user40276 | This is defninetly not enough. The local theory is basically understanding spectra (stable stuff), simplicial rings and dg stuff. And none of these topics is contained in HTT. | |
| Sep 13, 2015 at 22:53 | comment | added | user62675 | Higher Algebra is also an important resource to the algebra of stable homotopy theory and derived algebraic geometry. | |
| S Sep 13, 2015 at 21:02 | history | answered | Yonatan Harpaz | CC BY-SA 3.0 | |
| S Sep 13, 2015 at 21:02 | history | made wiki | Post Made Community Wiki by Yonatan Harpaz |