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- W1577315997 abstract "In this paper we prove that any sheaf of modules over any topological space (in fact, any <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper O> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>O</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {O}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-module where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper O> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>O</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {O}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a sheaf of rings on the topological space) has a flat cover and a cotorsion envelope. This result is very useful, as we shall explain later in the introduction, in order to compute cohomology, due to the fact that the category of sheaves (<inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper O> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>O</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {O}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-modules) does not have in general enough projectives." @default.
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- W1577315997 date "2001-10-24" @default.
- W1577315997 modified "2023-09-26" @default.
- W1577315997 title "Flat covers and cotorsion envelopes of sheaves" @default.
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