Relative subanalytic sheaves
Volume 226 / 2014
Fundamenta Mathematicae 226 (2014), 79-99
MSC: 18F10, 18F20, 32B20.
DOI: 10.4064/fm226-1-5
Abstract
Given a real analytic manifold $Y$, denote by $Y_{\rm sa}$ the associated subanalytic site. Now consider a product $Y=X\times S$. We construct the endofunctor $\mathcal {F}\mapsto \mathcal {F}^{S}$ on the category of sheaves on $Y_{\rm sa}$ and study its properties. Roughly speaking, $\mathcal {F}^S$ is a sheaf on $X_{\rm sa}\times S$. As an application, one can now define sheaves of functions on $Y$ which are tempered or Whitney in the relative sense, that is, only with respect to $X$.
