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Relative subanalytic sheaves

Volume 226 / 2014

Teresa Monteiro Fernandes, Luca Prelli 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 $X$.

Authors

  • Teresa Monteiro FernandesCentro de Matemática e Aplicações Fundamentais
    e Departamento de Matemática da FCUL, Complexo 2
    2 Avenida Prof. Gama Pinto
    1649-003, Lisboa, Portugal
    e-mail
  • Luca PrelliCentro de Matemática e Aplicações Fundamentais
    e Departamento de Matemática da FCUL, Complexo 2
    2 Avenida Prof. Gama Pinto
    1649-003, Lisboa, Portugal
    e-mail

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