Real spectrum with Nash structural sheaf. (English) Zbl 1062.14070

Using the definition of Nash structural sheaf over the real spectrum of a commutative ring given by M.-F. Roy [in: Geométrie algébrique réelle et formes quadratiques, Lect. Notes Math. 959, 406–432 (1982; Zbl 0497.14009)] the author shows that the Nash structural sheaf is determined only by the underlying topological space. He gives easy descriptions of a stalk of this Nash sheaf and sections of this sheaf over an open basis. He also calculates the stalks and global sections of it in a restricted case. As an application, the author investigates some basic properties of “separated” morphisms of real schemes.


14P20 Nash functions and manifolds
13J30 Real algebra


Zbl 0497.14009
Full Text: DOI Euclid


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