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- W4292003192 abstract "We prove that the $v_1$-local $G$-equivariant stable homotopy category for $G$ a finite group has a unique $G$-equivariant model at $p=2$. This means that at the prime $2$ the homotopy theory of $G$-spectra up to fixed point equivalences on $K$-theory is uniquely determined by its triangulated homotopy category and basic Mackey structure. The result combines the rigidity result for $K$-local spectra of the second author with the equivariant rigidity result for $G$-spectra of the first author. Further, when the prime $p$ is at least $5$ and does not divide the order of $G$, we provide an algebraic exotic model as well as a $G$-equivariant exotic model for the $v_1$-local $G$-equivariant stable homotopy category, showing that for primes $p ge 5$ equivariant rigidity fails in general." @default.
- W4292003192 created "2022-08-16" @default.
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- W4292003192 date "2017-05-10" @default.
- W4292003192 modified "2023-09-23" @default.
- W4292003192 title "Rigidity and exotic models for $v_1$-local $G$-equivariant stable homotopy theory" @default.
- W4292003192 doi "https://doi.org/10.48550/arxiv.1705.03855" @default.
- W4292003192 hasPublicationYear "2017" @default.
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