@misc{den-22-theory-junk,
  author = {Deninger, Christopher},
  title = {Dynamical Systems for Arithmetic Schemes},
  howpublished = {arXiv preprint},
  number = {1807.06400, version 3},
  url = {https://arxiv.org/abs/1807.06400},
  year = 2022,
  pages = {},
  month = jan,
  doi = {10.48550/arXiv.1807.06400},
  comment = {Nothing to do with our AA.},
  abstract = {Motivated by work of Kucharczyk and Scholze, we use sheafified rational Witt vectors to attach a new ringed space $W_{\mathrm{rat}}(X)$ to every scheme $X$. We also define $R$-valued points $W_{\mathrm{rat}}(X)(R)$ of $W_{\mathrm{rat}}(X)$ for every commutative ring R. For normal schemes $X$ of finite type over $\mathrm{spec}\mathbb{Z}$, using $W_{\mathrm{rat}}(X)(\mathbb{C})$ we construct infinite dimensional $\mathbb{C}$-dynamical systems whose periodic orbits are related to the closed points of $X$. Various aspects of these topological dynamical systems are studied. We also explain how certain p-adic points of $W_{\mathrm{rat}}(X)$ for $X$ the spectrum of a $p$-adic local number ring are related to the points of the Fargues-Fontaine curve. The new intrinsic construction of the dynamical systems generalizes and clarifies the original extrinsic construction in v.1 and v.2. Many further results have been added.}
}