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.
2022-01-01
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:
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