Timeline for Why is it useful for the (relative) Picard functor to be representable?
Current License: CC BY-SA 3.0
9 events
when toggle format | what | by | license | comment | |
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Nov 6, 2016 at 15:50 | vote | accept | user8329099 | ||
Nov 5, 2016 at 4:44 | comment | added | Sándor Kovács | It is useful for pretty much any functor to be representable. | |
Nov 4, 2016 at 21:12 | comment | added | user8329099 | @ndfc23: Thanks, I'll definitely look into FGA Explained. | |
Nov 4, 2016 at 21:04 | answer | added | Piotr Achinger | timeline score: 6 | |
Nov 4, 2016 at 16:14 | comment | added | nfdc23 | Why were you studying that Chapter 8 if you hadn't been told about a reason why such things are useful? Anyway, look at the chapter (with many historical comments) on Picard schemes by Kleiman in the book "FGA Explained", and contemplate the meaning of Jacobians of smooth proper curves which may not have rational points and how one might relativize that for curves over a base (esp. when some fibers are not smooth). Mazur's work on torsion in elliptic curves over $\mathbf{Q}$ is a glorious application of the latter. | |
Nov 4, 2016 at 15:43 | comment | added | Francesco Polizzi | In general, representability is roughly speaking related to the existence of a moduli space for the deformation functor you are considering. | |
Nov 4, 2016 at 15:02 | history | edited | user8329099 |
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Nov 4, 2016 at 14:57 | review | First posts | |||
Nov 4, 2016 at 15:17 | |||||
Nov 4, 2016 at 14:56 | history | asked | user8329099 | CC BY-SA 3.0 |