$q$-Witt vectors and $q$-Hodge complexes

Ferdinand Wagner

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arXiv · 2410.23078

$q$-Witt vectors and $q$-Hodge complexes

Ferdinand Wagner

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Abstract

In this article, we'll introduce a $q$-variant of Witt vectors and de Rham-Witt complexes. This variant is closely related to the Habiro ring of a number field constructed by Garoufalidis, Scholze, Wheeler, and Zagier, to $q$-Hodge cohomology, and to $\operatorname{THH}(-/\mathrm{ku})$. While most of these connections will only be explored in forthcoming work, the goal of this article is to provide the necessary technical foundation.

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Ferdinand Wagner. 2024-10-30. $q$-Witt vectors and $q$-Hodge complexes. https://arxiv.org/abs/2410.23078

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