{"paper":{"title":"Pure Projective Tilting Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Ivo Herzog, Jan Trlifaj, Jan \\v{S}aroch, Pavel P\\v{r}\\'ihoda, Silvana Bazzoni","submitted_at":"2017-03-14T22:06:22Z","abstract_excerpt":"Let $T$ be a $1$-tilting module whose tilting torsion pair $({\\mathcal T}, {\\mathcal F})$ has the property that the heart ${\\mathcal H}_t$ of the induced $t$-structure (in the derived category ${\\mathcal D}({\\rm Mod} \\mbox{-} R)$ is Grothendieck. It is proved that such tilting torsion pairs are characterized in several ways: (1) the $1$-tilting module $T$ is pure projective; (2) ${\\mathcal T}$ is a definable subcategory of ${\\rm Mod} \\mbox{-} R$ with enough pure projectives, and (3) both classes ${\\mathcal T}$ and ${\\mathcal F}$ are finitely axiomatizable.\n  This study addresses the question o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04745","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"}