Real spectrum with Nash structural sheaf
Masato Fujita
Source: Proc. Japan Acad. Ser. A Math. Sci.
Volume 79, Number 2
(2003), 36-41.
Abstract
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.
Primary Subjects: 13J30
Secondary Subjects: 14P20
Keywords: Real spectrum; Nash structural sheaf
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.pja/1116443606
Mathematical Reviews number (MathSciNet):
MR1960741
Zentralblatt MATH identifier:
1062.14070
Digital Object Identifier: doi:10.3792/pjaa.79.36
References
Alonso, M. E., and Roy, M.-F.: Real strict localisation. Math. Z., 194 (3), 429--441 (1987).
Mathematical Reviews (MathSciNet):
MR879943
Coste, M., Ruiz, M., and Shiota, M.: Uniform bounds on complexity and transfer of global properties of Nash functions. J. Reine Angew. Math., 536, 209--235 (2001).
Hartshorne, R.: Algebraic Geometry. Springer-Verlag, New York-Heidelberg (1977).
Mathematical Reviews (MathSciNet):
MR463157
Coste, M., Bochnak, J., and Roy, M.-F.: Real Algebraic Geometry. Translated from the 1987 french original ``Géométrie Algébrique Réele''. Springer-Verlag, Berlin (1998).
Matsumura, H.: Commutative Ring Theory. Translated from the Japanese by Reid, M. Cambridge Univ. Press, Cambridge (1986).
Mathematical Reviews (MathSciNet):
MR879273
Raynaud, M.: Anneaux locaux henséliens. Lecture Note in Math. vol. 169, Springer-Verlag, Berlin-New York, pp. 1--129 (1970).
Mathematical Reviews (MathSciNet):
MR277519
Roy, M.-F.: Faisceau Structual sur le spectre réel et functions de Nash. Real Algebraic Geometry and Quadratic Forms. Lecture Note in Math. vol. 959, Springer-Verlag, Berlin-New York, pp. 406--432 (1982).
