We show that the Nash structural sheaf over the real spectrum of a commutative ring is determined only by the underlying space. We also calculate the stalks and global sections of it in the restricted case. As an application, we show some basic properties of `separated' morphisms.
Masato Fujita. "Real spectrum with Nash structural sheaf." Proc. Japan Acad. Ser. A Math. Sci. 79 (2) 36 - 41, Feb. 2003. https://doi.org/10.3792/pjaa.79.36