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arXiv · 1904.03156

On the decomposition of the De Rham complex on formal schemes

Leovigildo Alonso·Ana Jeremias·Marta Perez
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Abstract

We show that, for a pseudo-proper smooth noetherian formal scheme $\mathfrak{X}$ over a positive characteristic $p$ field, its truncated De Rham complex up to the characteristic $p$ is decomposable. Moreover, if the dimension of $\mathfrak{X}$ is exactly $p$, then the full De Rham complex is decomposable. Along the way we establish the Cartier isomorphism associated to a smooth morphism of positive characteristic noetherian formal schemes.

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Leovigildo Alonso, Ana Jeremias, Marta Perez. 2019-04-05. On the decomposition of the De Rham complex on formal schemes. https://doi.org/10.1512/iumj.2021.70.8574

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