Timeline for Algebraic geometry used "externally" (in problems without obvious algebraic structure).
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Mar 9 at 14:31 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Jun 23, 2010 at 21:03 | history | edited | Daniel Litt | CC BY-SA 2.5 |
added 19 characters in body
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| Jun 23, 2010 at 20:42 | comment | added | CFZ | Aut(S_6) embeds in $M_{12}$ but I think that only for $M_24$ is it known how to build the entire group canonically over a finite field. My "thoughts", however, are very limited because I don't know much about finite groups. | |
| Jun 23, 2010 at 20:33 | comment | added | Daniel Litt | Interesting--I have heard rumors of a story connecting the outer automorphism of $S_6$ to the Mathieu group $M_{12}$, which is the automorphism group of the unique Steiner system $(5, 6, 12)$. A possible connection? | |
| Jun 23, 2010 at 20:24 | comment | added | CFZ | Generally, for any interesting combinatorial object there is a desire to construct it (or $q$-deform / quantize it, find coverings and automorphisms, etc) using geometry over finite fields. For example, the outer automorphism of $S_6$ can be understood using geometry mod 5, and other special finite groups can be realized as (linear or projective) algebraic groups over finite fields. | |
| Jun 23, 2010 at 20:07 | comment | added | Daniel Litt | I hadn't seen Goppa codes (before wikipedia'ing them just now)---this is quite nice. | |
| Jun 23, 2010 at 19:58 | comment | added | CFZ | (I mean Goppa codes and the later refinements, nor error correcting codes in general; most codes don't come from algebraic geometry.) | |
| Jun 23, 2010 at 19:56 | comment | added | CFZ | Error-correcting codes are a similar example, of constructing combinatorial objects from varieties over finite fields. | |
| Jun 23, 2010 at 19:53 | history | answered | Daniel Litt | CC BY-SA 2.5 |