Let $N:=textrm{Neigh}_{Nis}(U,nu)$ denote the filtered category of Nisnevich neighborhoods of the point $nuin U$. Then $textrm{colim}_{Vin N^{op}} Vcong textrm{spec}(mathcal{O}^{h}_{U,nu})$, where $N^{op}$ denotes the opposite category of $N$ and $mathcal{O}^{h}_{U,nu}$ is the henselization of the local ring $mathcal{O}_{U,nu}$.
My guess now would be that the fiber is the constant simplicial set associated to the set $textrm{Hom}_{k}(textrm{spec}(mathcal{O}^{h}_{U,nu}),X)$.
Maybe someone can clarify this as well as your second question.
No comments:
Post a Comment