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arXiv · 1810.04134

Localizations and completions in motivic homotopy theory

Lorenzo Mantovani
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Abstract

Let $K$ be a perfect field and let $E$ be a homotopy commutative ring spectrum in the Morel-Voevodsky stable motivic homotopy category $\mathcal{SH}(K)$. In this work we investigate the relation between the $E$-homology localization and $E$-nilpotent completion of a spectrum X. Under reasonable assumptions on $E$ and $X$ we show that these two operations coincide and can be expressed in terms of formal completions or localizations in the usual sense of commutative algebra. We deduce convergence criteria for the $E$-based motivic Adams-Novikov spectral sequence.

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Lorenzo Mantovani. 2018-10-09. Localizations and completions in motivic homotopy theory. https://arxiv.org/abs/1810.04134

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