{"paper":{"title":"Matrix factorizations and motivic measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RT"],"primary_cat":"math.AG","authors_text":"Olaf M. Schn\\\"urer, Valery A. Lunts","submitted_at":"2013-10-28T22:23:00Z","abstract_excerpt":"This article is the continuation of [LS12]. We use categories of matrix factorizations to define a morphism of rings (= a Landau-Ginzburg motivic measure) from the (motivic) Grothendieck ring of varieties over $\\mathbb{A}^1$ to the Grothendieck ring of saturated dg categories (with relations coming from semi-orthogonal decompositions into admissible subcategories). Our Landau-Ginzburg motivic measure is the analog for matrix factorizations of the motivic measure in [BLL04] whose definition involved bounded derived categories of coherent sheaves. On the way we prove smoothness and a Thom-Sebast"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7640","kind":"arxiv","version":2},"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"}