{"paper":{"title":"Some comments on motivic nilpotence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Jens Hornbostel","submitted_at":"2015-11-23T16:07:52Z","abstract_excerpt":"We discuss some results and conjectures related to the existence of the non-nilpotent motivic maps $\\eta$ and $\\mu_9$. To this purpose, we establish a theory of power operations for motivic $H_{\\infty}$-spectra. Using this, we show that the naive motivic analogue of the unstable Kahn-Priddy theorem fails. Over the complex numbers, we show that the motivic $T$-spectrum $S[\\eta^{-1},\\mu_9^{-1}]$ is closely related to higher Witt groups, where $S$ is the motivic sphere spectrum and $\\eta$, $\\sigma$ and $\\mu_9$ are explicit elements in $\\pi_{**}(S)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07292","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}