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


Abstract in English

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 complete

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