{"paper":{"title":"A finer Tate duality theorem for local Galois symbols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Evangelia Gazaki","submitted_at":"2017-03-20T21:25:22Z","abstract_excerpt":"Let $K$ be a finite extension of $\\mathbb{Q}_p$. Let $A$, $B$ be abelian varieties over $K$ of good reduction. For any integer $m\\geq 1$, we consider the Galois symbol $K(K;A,B)/m\\rightarrow H^2(K,A[m]\\otimes B[m])$, where $K(K;A,B)$ is the Somekawa $K$-group attached to $A,B$. This map is a generalization of the Galois symbol $K_2^M(K)/m\\rightarrow H^2(K,\\mu_m^{\\otimes 2})$ of the Bloch-Kato conjecture, where $K_2^M(K)$ is the Milnor $K$-group of $K$. In this paper we give a geometric description of the image of this generalized Galois symbol by looking at the Tate duality pairing $H^{2}(K,A["},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06974","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"}