Description

Book Synopsis
Explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by $C^\infty $-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are $C^\infty $-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps.

Table of Contents
  • Introduction
  • $C^\infty$-rings
  • The $C^\infty$-ring $C^\infty (X)$ of a manifold $X$
  • $C^\infty $-ringed spaces and $C^\infty $-schemes
  • Modules over $C^\infty$-rings and $C^\infty $-schemes
  • $C^\infty $-stacks
  • Deligne-Mumford $C^\infty $-stacks
  • Sheaves on Deligne-Mumford $C^\infty $-stacks
  • Orbifold strata of $C^\infty $-stacks
  • Appendix A. Background material on stacks
  • Bibliography
  • Glossary of Notation
  • Index.

    Algebraic Geometry over Cinfty Rings

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      A Paperback by Dominic Joyce

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        Publisher: MP-AMM American Mathematical
        Publication Date: Publication Date: 10/30/2019 12:00:00 AM
        ISBN13: 9781470436452, 978-1470436452
        ISBN10: 1470436450
        Also in:
        Algebraic geometry Geometry

        Description

        Book Synopsis
        Explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by $C^\infty $-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are $C^\infty $-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps.

        Table of Contents
        • Introduction
        • $C^\infty$-rings
        • The $C^\infty$-ring $C^\infty (X)$ of a manifold $X$
        • $C^\infty $-ringed spaces and $C^\infty $-schemes
        • Modules over $C^\infty$-rings and $C^\infty $-schemes
        • $C^\infty $-stacks
        • Deligne-Mumford $C^\infty $-stacks
        • Sheaves on Deligne-Mumford $C^\infty $-stacks
        • Orbifold strata of $C^\infty $-stacks
        • Appendix A. Background material on stacks
        • Bibliography
        • Glossary of Notation
        • Index.

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