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Relative subanalytic sheaves

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Monteiro Fernandes T., Prelli L.

Fundamenta Mathematicae

2014

tom 226

nr 1

79-99

Given a real analytic manifold Y, denote by $Y_{sa}$ the associated subanalytic site. Now consider a product Y = X × S. We construct the endofunctor $ℱ ↦ ℱ^{S}$ on the category of sheaves on $Y_{sa}$ and study its properties. Roughly speaking, $ℱ^{S}$ is a sheaf on $X_{sa} × S$. 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.

Grauert's theorem for subanalytic open sets in real analytic manifolds

100%

Barlet D., Monteiro Fernandes T.

Studia Mathematica

2011

tom 204

nr 3

265-274

By an open neighbourhood in ℂⁿ of an open subset Ω of ℝⁿ we mean an open subset Ω' of ℂⁿ such that ℝⁿ ∩ Ω' = Ω. A well known result of H. Grauert implies that any open subset of ℝⁿ admits a fundamental system of Stein open neighbourhoods in ℂⁿ. Another way to state this property is to say that each open subset of ℝⁿ is Stein. We shall prove a similar result in the subanalytic category: every subanalytic open subset in a paracompact real analytic manifold M admits a fundamental system of subanalytic Stein open neighbourhoods in any complexification of M.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Studia Mathematica

2 Monteiro Fernandes T.

1 Barlet D.

1 Prelli L.

1 2014

1 2011

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Relative subanalytic sheaves

Grauert's theorem for subanalytic open sets in real analytic manifolds