{"paper":{"title":"Semistable reduction in characteristic 0","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Gaku Liu, Karim Adiprasito, Michael Temkin","submitted_at":"2018-10-07T12:20:26Z","abstract_excerpt":"In 2000 Abramovich and Karu proved that any dominant morphism $f\\:X\\to B$ of varieties of characteristic zero can be made weakly semistable by replacing $B$ by a smooth alteration $B'$ and replacing the proper transform of $X$ by a modification $X'$. In the language of log geometry this means that $f'\\:X'\\to B'$ is log smooth and saturated for appropriate log structures. Moreover, Abramovich and Karu formulated a stronger conjecture that $f'\\:X'\\to B'$ can be even made semistable, which amounts to making $X'$ smooth as well, and explained why this is the best resolution of $f$ one might hope f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03131","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"}