{"paper":{"title":"\\'{E}tale Homotopy Obstructions of Arithmetic Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Edo Arad, Shachar Carmeli, Tomer M. Schlank","submitted_at":"2019-02-09T10:48:55Z","abstract_excerpt":"Let $K$ be a field of characteristic $\\ne 2$ and let $X$ be the affine variety over $K$ defined by the equation $$ X:\\ a_0x_0^2 + \\cdots + a_nx_n^2 = 1 $$ where $n\\ge 0$ and $a_i\\in K$. In this paper we compute the lowest mod 2 \\'{e}tale homological obstruction class to the existence of a $K$-rational point on $X$, and show that it is the cup product of the form $$ o_{n+1} = [a_0]\\cup\\cdots\\cup[a_n]. $$\n  Our computation is an \\'{e}tale-homotopy analogue of the topological fact that Stiefel-Whitney classes are the homological obstructions to find a section to the unit sphere bundle of a real v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03404","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"}