We study thick ideals in the stable motivic homotopy category SH(k) and in its subcategories of compact and of finite cellular objects. If k is a subfield of the complex or even the real numbers, then using comparison functors we find thick ideals corresponding to thick ideals in classical or Z/2-equivariant stable homotopy theory, respectively. We also study motivic Morava K-theories AK(n), for which we prove the motivic analogue of the decomposition of the Bousfield class of E(n) into Bousfield classes of K(i)’s over the complex numbers if p>2. In that case we also prove that AK(n)-acyclicity implies AK(n-1)-acyclicity.
CITATION STYLE
Joachimi, R. (2020). Thick ideals in equivariant and motivic stable homotopy categories. In Springer Proceedings in Mathematics and Statistics (Vol. 309, pp. 109–219). Springer. https://doi.org/10.1007/978-981-15-1588-0_6
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