Lemma 28.13.5. Let X be a scheme. The following are equivalent:
The scheme X is universally Japanese.
For every affine open U \subset X the ring \mathcal{O}_ X(U) is universally Japanese.
There exists an affine open covering X = \bigcup U_ i such that each \mathcal{O}_ X(U_ i) is universally Japanese.
There exists an open covering X = \bigcup X_ j such that each open subscheme X_ j is universally Japanese.
Moreover, if X is universally Japanese then every open subscheme is universally Japanese.
Comments (0)