Corpus ID: 204905120

Hodge-to-de Rham degeneration for stacks

@article{Kubrak2019HodgetodeRD,
  title={Hodge-to-de Rham degeneration for stacks},
  author={Dmitry Kubrak and A. Prikhodko},
  journal={arXiv: Algebraic Geometry},
  year={2019}
}
We introduce a notion of a Hodge-proper stack and extend the method of Deligne-Illusie to prove the Hodge-to-de Rham degeneration in this setting. In order to reduce the statement in characteristic $0$ to characteristic $p$, we need to find a good integral model of a stack (a so-called spreading), which, unlike in the case of schemes, need not to exist in general. To address this problem we investigate the property of spreadability in more detail by generalizing standard spreading out results… Expand

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