{"paper":{"title":"Bott periodicity in the Hit Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Shaun V. Ault","submitted_at":"2014-06-30T13:44:49Z","abstract_excerpt":"In this short note, we use Robert Bruner's $\\mathcal{A}(1)$-resolution of $P = \\mathbb{F}_2[t]$ to shed light on the Hit Problem. In particular, the reduced syzygies $P_n$ of $P$ occur as direct summands of $\\widetilde{P}^{\\otimes n}$, where $\\widetilde{P}$ is the augmentation ideal of the map $P \\to \\mathbb{F}_2$. The complement of $P_n$ in $\\widetilde{P}^{\\otimes n}$ is free, and the modules $P_n$ exhibit a type of \"Bott Periodicity\" of period $4$: $P_{n+4} = \\Sigma^8P_n$. These facts taken together allow one to analyze the module of indecomposables in $\\widetilde{P}^{\\otimes n}$, that is, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7734","kind":"arxiv","version":2},"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"}