Abstract:In this short note, we prove a general nilpotence theorem for a rational rigid 2-ring all of whose objects satisfy a certain ``moderate growth condition'' inspired from the theory of tensor categories. This applies in particular to the category of modules over a rational $E_{\infty}$-ring, to the derived category of any super-Tannakian category in characteristic zero, and conjecturally to Voevodsky's rational category of mixed motives over a field $DM_{\mathbb{Q}}$. In fact, we further prove that any such category has enough tt-fields, which can be chosen to be of the form Perf(L) for an even 2-periodic field L.
| Comments: | 22 pages, comments very welcome! |
| Subjects: | Algebraic Geometry (math.AG); Algebraic Topology (math.AT); Category Theory (math.CT); Representation Theory (math.RT) |
| Cite as: | arXiv:2605.24637 [math.AG] |
| (or arXiv:2605.24637v1 [math.AG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24637 arXiv-issued DOI via DataCite (pending registration) |
From: Logan Hyslop [view email]
[v1]
Sat, 23 May 2026 15:56:16 UTC (10,776 KB)
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