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I have two questions about the classical exponential sheaf sequence :

Q1. In their book "Compact Complex surfaces", the authors (Barth, Hulek, Peters, Van de Ven) generalize the exponential sheaf sequence for smooth curves to non reduced singular complex curves. Can we generalize this construction for non reduced singular subscheme of higher dimension ?

Q2. Is there an analoguous of the exponential sheaf sequence in positive characteristic ?

Thank you !

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    $\begingroup$ In principle, I don't see a problem for Q1, although I can't really check what they do, since my copy is not with me at the moment. The answer to Q2 is probably no. Although the Kummer sequence in the etale topology is a sort of consolation prize. $\endgroup$
    – Donu Arapura
    Feb 28, 2012 at 16:26
  • $\begingroup$ A reference for the exponential exact sequence on arbitrary complex spaces (hence on analytifications of arbitrary complex varieties) is [Kaup-Kaup, Holomorphic functions of several variables, Lemma 54.3]. $\endgroup$
    – Olivier Benoist
    Oct 16, 2018 at 6:31

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