{"paper":{"title":"On a Filtration of CH_{0} for an Abelian Variety A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Evangelia Gazaki","submitted_at":"2013-05-27T18:16:34Z","abstract_excerpt":"Let $A$ be an abelian variety defined over a field $k$. In this paper we define a filtration $F^{r}$ of the group $CH_{0}(A)$ and prove an isomorphism $\\frac{K(k;A,...,A)}{\\Sym}\\otimes\\mathbb{Z}[\\frac{1}{r!}]\\simeq F^{r}/F^{r+1}\\otimes\\mathbb{Z}[\\frac{1}{r!}]$, where $K(k;A,...,A)$ is the Somekawa K-group attached to $r$-copies of the abelian variety $A$.\\\\ In the special case when $k$ is a finite extension of $\\mathbb{Q}_{p}$ and $A$ has split multiplicative reduction, we compute the kernel of the map $CH_{0}(A)\\otimes\\Z[\\frac{1}{2}]\\rightarrow \\rm{Hom}(Br(A),\\Q/\\Z)\\otimes\\Z[\\frac{1}{2}]$, in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6284","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"}