Let X be a regular tame stack. If X is locally of finite type over a field, we prove that the essential dimension of X is equal to its generic essential dimension; this generalizes a previous result of P. Brosnan, Z. Reichstein and the second author. Now suppose that X is locally of finite type over a 1-dimensional noetherian local domain R with fraction field K and residue field k. We prove that edk Xk ≤ edK XK if X → Spec R is smooth and edk Xk ≤ edK XK + 1 in general.
The genericity theorem for the essential dimension of tame stacks
Bresciani G.;Vistoli A.
2022
Abstract
Let X be a regular tame stack. If X is locally of finite type over a field, we prove that the essential dimension of X is equal to its generic essential dimension; this generalizes a previous result of P. Brosnan, Z. Reichstein and the second author. Now suppose that X is locally of finite type over a 1-dimensional noetherian local domain R with fraction field K and residue field k. We prove that edk Xk ≤ edK XK if X → Spec R is smooth and edk Xk ≤ edK XK + 1 in general.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Genericity-rivisto7.pdf
accesso aperto
Tipologia:
Accepted version (post-print)
Licenza:
Solo Lettura
Dimensione
349.81 kB
Formato
Adobe PDF
|
349.81 kB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
