C [infinity]-differentiable spaces
By: Juan A. Navarro González, Juan B. Sancho de Salas.
Contributors: Sancho de Salas, Juan B., 1957-
Series: Lecture notes in mathematics -- 1824; Lecture notes in mathematics (Springer-Verlag) -- 1824.
Publisher: Springer
Published: 2003
Place of publication: Berlin; New York
Language: eng
Number of pages: 188
Subjects: Differentiable manifolds; Algebraic spaces; Topological rings
Other titles: C-differentiable spaces
Description: The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Fréchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of C \infinity-rings and C \infinity-schemes, as well as in the framework of Spallek’s C \infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Fréchet spaces.
Notes: On t.p. [infinity] appears as the infinity symbol at superscript position.

Includes bibliographical references (p. [181]-183) and index.