Timeline for Applications of Stacks
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Oct 17, 2010 at 17:15 | comment | added | Qfwfq | I haven't met stacks often, but I used to think that they are tautological reformulations of: a) moduli problems b) quotient problems, that allow to "speak geometrically" (e.g. a moduli stack has a tangent bundle, a "moduli problem" doesn't) | |
| Oct 17, 2010 at 1:09 | comment | added | BCnrd | Cohomology of stacks provide useful "algebraic/arithmetic" constructions superior in some respects to what can be done using coarse moduli schemes. For example, if one wants to equip spaces of modular forms with $\mathbf{Z}$-structure in a manner that handles all primes in a unified manner, it can be simpler to work with moduli stacks of (generalized) elliptic curves rather than adjoining "extra level" and using fine moduli schemes. For example "$X_0(N)$" is always a regular proper Artin stack, whereas the coarse moduli scheme cousin is neither regular nor fine (but is also useful!). | |
| Oct 16, 2010 at 15:38 | answer | added | Greg Muller | timeline score: 10 | |
| Oct 16, 2010 at 15:16 | answer | added | user1504 | timeline score: 14 | |
| Oct 16, 2010 at 14:51 | history | edited | James D. Taylor |
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| Oct 16, 2010 at 14:29 | history | asked | James D. Taylor | CC BY-SA 2.5 |