Timeline for Definition of locally symmetric space of reductive groups
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| May 8, 2023 at 20:04 | history | edited | RobPratt | CC BY-SA 4.0 |
edited tags; edited title
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| May 8, 2023 at 17:41 | history | became hot network question | |||
| May 8, 2023 at 17:22 | vote | accept | Coherent Sheaf | ||
| May 8, 2023 at 16:57 | answer | added | David Loeffler | timeline score: 13 | |
| May 8, 2023 at 15:13 | comment | added | LSpice |
TeX note: $\Gamma\setminus X$ \Gamma\setminus X, as the name suggests, is for set difference. For the quotient space, you want $\Gamma\backslash X$ \Gamma\backslash X. I edited accordingly.
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| May 8, 2023 at 15:12 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading
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| May 8, 2023 at 14:36 | comment | added | Moishe Kohan | This is not the most general definition of a locally symmetric space. | |
| May 8, 2023 at 13:56 | comment | added | Donu Arapura | I'm far from an expert, but I think it is helpful to start with examples, which have rich and beautiful geometries. In the simplest case: $G=SL_2$, then $X= SL_2(\mathbb{R})/SO_2$ is the upper half plane. Then $X(\Gamma)$ would include modular curves. In the next simplest case, $G$ is the Weil restriction of $SL_2$ of a real quadratic field, and $X(\Gamma)$ would be a Hilbert modular surface.... | |
| May 8, 2023 at 13:03 | comment | added | Coherent Sheaf | @MarsaultChabat both. | |
| May 8, 2023 at 13:00 | comment | added | Marsault Chabat | No I'm asking if wether you want information about X or information about Gamma\X or both of them? | |
| May 8, 2023 at 12:47 | comment | added | Coherent Sheaf | @MarsaultChabat yes, I am trying to find some motivation so that I can create a better picture in my head. For instance, when someone sees a redictive group, I don't think it is very natural to think that we should try and understand the geoemetry of this quotient. Or is it natural? | |
| May 8, 2023 at 11:16 | comment | added | Marsault Chabat | Are you asking for a (motivating) reason for defining symmetric space, locally symmetric space, or both? | |
| May 8, 2023 at 11:13 | comment | added | Mikhail Borovoi | See also papers referring to these two, expecially those by J. S. Milne. | |
| May 8, 2023 at 10:52 | comment | added | Mikhail Borovoi | See also: Deligne, Pierre Variétés de Shimura: interprétation modulaire, et techniques de construction de modèles canoniques. (French) Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, pp. 247–289, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979. | |
| May 8, 2023 at 10:51 | comment | added | Mikhail Borovoi | Some Shimura varieties (those of abelian type) classify abelian varieties with additional structure. See: Deligne, Pierre Travaux de Shimura. (French) Séminaire Bourbaki, 23ème année (1970/1971), Exp. No. 389, pp. 123–165. Lecture Notes in Math., Vol. 244, Springer, Berlin, 1971. | |
| May 8, 2023 at 9:40 | history | asked | Coherent Sheaf | CC BY-SA 4.0 |