{"paper":{"title":"Tor as a Module over an Exterior Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"David Eisenbud, Frank-Olaf Schreyer, Irena Peeva","submitted_at":"2018-10-11T13:14:26Z","abstract_excerpt":"Let $S$ be a regular local ring with residue field $k$ and let $M$ be a finitely generated $S$-module. Suppose that $f_1,\\dots ,f_c\\in S$ is a regular sequence that annihilates $M$, and let $E$ be an exterior algebra over $k$ generated by $c$ elements.\n  The homotopies for the $f_{i}$ on a free resolution of $M$ induce a natural structure of graded $E$-module on ${\\rm Tor}^{S}(M,k)$. In the case where $M$ is a high syzygy over the complete intersectionR:=S/(f_{1},\\dots,f_{c})$ we describe this $E$-module structure in detail, including its minimal free resolution over $E$.\n  Turning to ${\\rm Ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04999","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"}