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arXiv · 2007.09857

THH and TC are (very) far from being homotopy functors

Elden Elmanto
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Abstract

We compute the $\mathbb{A}^1$-localization of several invariants of schemes namely, topological Hochschild homology ($\mathrm{THH}$), topological cyclic homology ($\mathrm{TC}$) and topological periodic cyclic homology ($\mathrm{TP}$). This procedure is quite brutal and kills the completed versions of most of these invariants. The main ingredient for the vanishing statements is the vanishing of $\mathbb{A}^1$-localization of de Rham cohomology (and, eventually, crystalline cohomology) in positive characteristics.

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Elden Elmanto. 2020-07-20. THH and TC are (very) far from being homotopy functors. https://arxiv.org/abs/2007.09857

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