Timeline for Can geometric point counting detect prime powers?
Current License: CC BY-SA 4.0
4 events
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| Nov 25, 2020 at 7:32 | comment | added | Gjergji Zaimi | I found a more modern reference that has essentially the same example, written in geometric language. See table 1 in the paper arxiv.org/abs/2007.16014 | |
| Nov 25, 2020 at 1:36 | comment | added | Gjergji Zaimi | @dhy There is a combinatorial construction in D. Glynn, "Rings of geometries II" J. Combin. Theory Ser. A 49 (1988), no. 1, 26-66. The author essentially shows that a certain polynomial of degree 14 gives a negative value at 6, but can be interpreted as counting the points of some variety. This variety is defined combinatorially, in a way that would allow you to define its points over a finite projective plane. The author uses this to prove the nonexistence of finite planes of order 6. Of course, no such example is known for $n>6$. | |
| Nov 25, 2020 at 0:32 | comment | added | dhy | Do you know of such a polynomial for say, $n=6$? | |
| Nov 25, 2020 at 0:02 | history | asked | Gjergji Zaimi | CC BY-SA 4.0 |