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# Questions tagged [kahler-differentials]

Kähler differentials provide an adaptation of differential forms to arbitrary commutative rings or schemes.

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### Example of closed non-exact torsion differential form on variety

I asked this question some time ago on MSE and received close to no interest. I feel it is appropriate for this site: I am interested in finding a particular example. I would like to find a variety (...
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### How to get a concrete description of $\pi_*\Omega_{X/S}(Z)|_Z$, when $X \supset Z \to S$ is a finite extension of Dedekind schemes?

Let $X/S$ be a proper, smooth relative curve over a Dedekind scheme $S$, for example, $X = \mathbb{P}^1_S \xrightarrow{\pi} S$. Suppose that $Z \to X$ is a horizontal effective Cartier divisor such ...
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### Logarithmic differentials on an arithmetic surface, and Poincaré residue

Suppose that $X$ is an arithmetic surface, i.e. $\pi: X \to S$ flat and relative dimension 1 over a Dedekind scheme $S$, and assume $X$ smooth. Let $Y \subset X$ be a horizontal effective Cartier ...
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### Confusion about the (Grothendieck–Poincaré) double dual of reflexive differentials vs usual differentials on a normal Cohen–Macaulay scheme

$\DeclareMathOperator\Hom{Hom}$Let $\mathcal{A}$ be an abelian category, my question is about the case when $\mathcal{A}$ is the category of quasi-coherent sheaves on a scheme $X$. There is a fully ...
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### $\Omega^1_{B_\bullet/A_\bullet}$ is acyclic if $A_\bullet \to B_\bullet$ is quasi-isomorphism

Let $A_\bullet \to B_\bullet$ be a quasi-isomorphism of simplicial rings in the sense of (P.62, I.3.1.7, Complexe Cotangent et Déformations I, Luc Illusie). Then, we define the simplicial $B_\bullet$-...
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### Kahler differentials and the m-adic filtration

Let $A$ be a comm. local $k$-algebra with max. ideal $m$. Let $gr(-)$ be the associated graded algebra or module for the $m$-adic filtration. The canonical derivation $d:A \to \Omega^1_A$ satisfies \$...
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