{"paper":{"title":"K-theory, genotypes, and biset functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT","math.KT"],"primary_cat":"math.GR","authors_text":"Serge Bouc (LAMFA)","submitted_at":"2016-04-26T14:57:34Z","abstract_excerpt":"Let p be an odd prime number. In this paper, we show that the genome $\\Gamma(P)$ of a finite $p$-group $P$, defined as the direct product of the genotypes of all rational irreducible representations of $P$, can be recovered from the first group of $K$-theory $K_1(\\mathbb{Q}P)$. It follows that the assignment $P \\to \\Gamma(P)$ is a $p$-biset functor. We give an explicit formula for the action of bisets on $\\Gamma$, in terms of generalized transfers associated to left free bisets. Finally, we show that $\\Gamma$ is a rational $p$-biset functor, i.e. that $\\Gamma$ factors through the Roquette cate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07703","kind":"arxiv","version":1},"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"}