Beyond perturbation 1: de Rham spaces

Abstract

It is shown that if one uses the notion of infinity nilpotent elements due to Moerdijk and Reyes, instead of the usual definition of nilpotents to define reduced $C^{\infty }$-schemes, the resulting de Rham spaces are given as quotients by actions of germs of diagonals, instead of the formal neighbourhoods of the diagonals.

Difference from the published version: formulation of Proposition 9 is corrected, a footnote and a reference are added

References in corpus (2)

• Quasi-coherent sheaves in differential geometry
• Beyond perturbation 2: asymptotics and Beilinson-Drinfeld Grassmannians in differential geometry

Cited by in corpus (7)

• Topics on Smooth Commutative Algebra
• A Universal Algebraic Survey of ${\mathcal{C}}^{\infty }-$Rings
• Quasi-coherent sheaves in differential geometry
• Separation Theorems in Smooth Commutative Algebra and Applications
• Beyond perturbation 2: asymptotics and Beilinson-Drinfeld Grassmannians in differential geometry
• On the order theory for ${\mathcal{C}}^{\infty }$-reduced ${\mathcal{C}}^{\infty }$-Rings and applications
• Von Neumann Regular ${\mathcal{C}}^{\infty }-$Rings and Applications