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I don't understand the definition of $\boldsymbol{\Omega}_A$ in the context of almost rings. In Gabber and Ramero https://arxiv.org/pdf/math/0409584.pdf it is covered in 9.6.12. How is $\boldsymbol{\Omega}_A$ defined? What is the difference to the usual Kähler module? I'm really sorry, but I'm lost.

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  • $\begingroup$ I see it for the first time, but the obvious difference is that $d_A:A\to\mathbf\Omega_A$ is not additive (the formula for $d_A(a+b)$ is just before 9.6.13) $\endgroup$ Oct 14, 2020 at 14:45
  • $\begingroup$ Fair, my issue is that I don't see what the definition of this object is and what the difference in the definition is. $\endgroup$ Oct 14, 2020 at 14:51
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    $\begingroup$ So I tried to answer the second of your questions. Because of non-additivity it comes out bigger than the Kähler module. $\endgroup$ Oct 14, 2020 at 15:00

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