{"paper":{"title":"Anisotropy and the integral closure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AC","authors_text":"Michiel Kosters","submitted_at":"2011-09-30T07:31:41Z","abstract_excerpt":"Let K be a number field and let A be an order in K. The trace map from K to Q induces a non-degenerate symmetric bilinear form <,>: B x B \\to Q/Z where B is a certain finite abelian group of size \\Delta(A). In this article we discuss how one can obtain information about \\mathcal{O}_K by purely looking at this symmetric bilinear form. The concepts of anisotropy and quasi-anisotropy, as defined in another article by the author, turn out to be very useful. We will for example show that under certain assumptions one can obtain \\mathcal{O}_K directly from <,>.\n  In this article we will work in a mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6733","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"}