{"paper":{"title":"Canonical tilting relative generators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Agnieszka Bodzenta, Alexey Bondal","submitted_at":"2017-01-30T21:31:12Z","abstract_excerpt":"Given a relatively projective birational morphism $f\\colon X\\to Y$ of smooth algebraic spaces with dimension of fibers bounded by 1, we construct tilting relative (over $Y$) generators $T_{X,f}$ and $S_{X,f}$ in $\\mathcal{D}^b(X)$. We develop a piece of general theory of strict admissible lattice filtrations in triangulated categories and show that $\\mathcal{D}^b(X)$ has such a filtration $\\mathcal{L}$ where the lattice is the set of all birational decompositions $f \\colon X \\xrightarrow{g} Z \\xrightarrow{h} Y$ with smooth $Z$. The $t$-structures related to $T_{X,f}$ and $S_{X,f}$ are proved t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08834","kind":"arxiv","version":4},"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"}