A Nilpotence Theorem for Rational Rigid 2-Rings of Moderate Growth
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910252255936512 |
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| author | Hyslop, Logan |
| author_facet | Hyslop, Logan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24637 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Nilpotence Theorem for Rational Rigid 2-Rings of Moderate Growth Hyslop, Logan Algebraic Geometry Algebraic Topology Category Theory Representation Theory 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. |
| title | A Nilpotence Theorem for Rational Rigid 2-Rings of Moderate Growth |
| topic | Algebraic Geometry Algebraic Topology Category Theory Representation Theory |
| url | https://arxiv.org/abs/2605.24637 |