{"paper":{"title":"Tate kernels, etale K-theory and the Gross kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kevin Hutchinson","submitted_at":"2017-09-19T14:42:29Z","abstract_excerpt":"For an odd prime $p$ and a number field $F$ containing a $p$th root of unity, we study generalised Tate kernels, $D_F^{[i,n]}$, for $i\\in \\mathbb{Z}$ and $n\\geq 1$, having the properties that if $i\\geq 2$ and if either $p$ does not divide $i$ or $\\mu_{p^n}\\subset F$ then there are natural isomorphisms $D_F^{[i,n]}\\cong K^{\\mbox{\\tiny \\'et}}_{2i-1}(O_F^S)/p^n$, and that they are periodic modulo a power of $p$ which depends on $F$ and $n$. Our main result is that if the Gross-Jaulent conjecture holds for $(F,p)$ then there is a natural isomorphism $D_F^{[i,n]}\\cong\\mathcal{E}_F/p^n$ where $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06465","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"}