Definition 34.10.1. Let $T$ be an affine scheme. A *standard V covering* is a finite family $\{ T_ j \to T\} _{j = 1, \ldots , m}$ with $T_ j$ affine such that for every morphism $g : \mathop{\mathrm{Spec}}(V) \to T$ where $V$ is a valuation ring, there is an extension $V \subset W$ of valuation rings (More on Algebra, Definition 15.123.1), an index $1 \leq j \leq m$, and a commutative diagram

\[ \xymatrix{ \mathop{\mathrm{Spec}}(W) \ar[r] \ar[d] & T_ j \ar[d] \\ \mathop{\mathrm{Spec}}(V) \ar[r]^ g & T } \]

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