Derived $\mathcal{O}_k$-adic geometry and derived Raynaud localization theorem
Abstract
The goal of the present text is to state and prove a generalization of Raynaud localization theorem in the setting of derived geometry. More explicitly, we show that the -category of quasi-paracompact and quasi-separated derived -analytic spaces can be realized as a localization of the -category of admissible derived formal schemes. We construct a derived rigidification functor generalizing Raynaud rigidification functor. In order to construct the latter we will need to formalize derived formal -adic formal geometry via a structured spaces approach. We prove that -adic Postnikov towers of derived -adic Deligne-Mumford stacks decompose and we relate these to Postnikov towers of derived -analytic spaces. This is possible by a precise comparison between the -adic cotangent complex and the -analytic cotangent complex.
Cite
@article{arxiv.1805.03302,
title = {Derived $\mathcal{O}_k$-adic geometry and derived Raynaud localization theorem},
author = {Jorge António},
journal= {arXiv preprint arXiv:1805.03302},
year = {2020}
}