{"paper":{"title":"The $\\ell$-adic trace formula for dg-categories and Bloch's conductor conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"B. To\\\"en, G. Vezzosi","submitted_at":"2016-05-28T22:28:11Z","abstract_excerpt":"Building on recent results by A. Blanc, M. Robalo and the authors, we present an $\\ell$-adic trace formula for smooth and proper dg-categories over a base $\\mathbb{E}_{\\infty}$-algebra $B$. We also give a variant when $B$ is only an $\\mathbb{E}_2$-algebra. As an application of this trace formula, we propose a strategy of proof of Bloch's conductor conjecture. This is a research announcement and detailed proofs will appear elsewhere."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08941","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"}