{"paper":{"title":"The Stable Equivalence and Cancellation Problems","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Jie-Tai Yu, Leonid Makar-Limanov, Peter van Rossum, Vladimir Shpilrain","submitted_at":"2003-10-05T19:17:59Z","abstract_excerpt":"Let $K$ be an arbitrary field of characteristic 0, and $\\Aff^n$ the $n$-dimensional affine space over $K$. A well-known cancellation problem asks, given two algebraic varieties $V_1, V_2 \\subseteq \\Aff^n$ with isomorphic cylinders $V_1 \\times \\Aff^1$ and $V_2 \\times \\Aff^1$, whether $V_1$ and $V_2$ themselves are isomorphic.\n In this paper, we focus on a related problem: given two varieties with equivalent (under an automorphism of $\\Aff^{n+1}$) cylinders $V_1 \\times \\Aff^1$ and $V_2 \\times \\Aff^1$, are $V_1$ and $V_2$ equivalent under an automorphism of $\\Aff^n$? We call this stable equivalen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0310060","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"}