Timeline for Chain of closed irreducible sets on Zariski Riemann spaces
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 8, 2020 at 10:44 | vote | accept | nowhere dense | ||
| Feb 7, 2020 at 13:19 | comment | added | Dario Spirito | I'm not sure. For algebras of finite type probably one can try by induction (if $K=\mathrm{Frac}(A)=F[x_1,\ldots,x_n]$, restrict everything to $F[x_1,\ldots,x_{n-1}]$, then to $F[x_1,\ldots.x_{n-2}], etc.: all dimensions should decrease by 1 each time), but I haven't worked it out. I also feel there should be an easier proof for arbitrary Noetherian rings. | |
| Feb 6, 2020 at 12:04 | comment | added | nowhere dense | Thanks, that is really interesting! Do you have any idea of what will happen when $A$ is an algebra of finite type over a field? In this case by Abhyankar's inequality the rational rank, and hence the rank, is bounded by the krull dimension of $A$, so we can't have the same type of obstruction. | |
| Feb 6, 2020 at 10:47 | history | answered | Dario Spirito | CC BY-SA 4.0 |