Relative subanalytic sheaves

Teresa Monteiro Fernandes¹ ; Luca Prelli¹

¹ Centro de Matemática e Aplicações Fundamentais e Departamento de Matemática da FCUL, Complexo 2 2 Avenida Prof. Gama Pinto 1649-003, Lisboa, Portugal

Fundamenta Mathematicae, Tome 226 (2014) no. 1, pp. 79-99.

Résumé

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 $X$.

Détail

DOI : 10.4064/fm226-1-5

Keywords: given real analytic manifold denote associated subanalytic site consider product times construct endofunctor mathcal mapsto mathcal category sheaves study its properties roughly speaking mathcal sheaf times application define sheaves functions which tempered whitney relative sense only respect