{"paper":{"title":"Motivic Landweber exact theories and their effective covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Marc Levine","submitted_at":"2014-01-01T13:48:45Z","abstract_excerpt":"Let $k$ be a field of characteristic zero and let $(F,R)$ be a Landweber exact formal group law. We consider a Landweber exact $T$-spectrum $\\mathcal{E}:=R\\otimes_{\\mathbb{L}}\\text{MGL}$ and its effective cover $f_0\\mathcal{E}\\to \\mathcal{E}$ with respect to Voevodsky's slice tower. The coefficient ring $R_0$ of $f_0\\mathcal{E}$ is the subring of $R$ consisting of elements of $R$ of non-positive degree; the power series $F\\in R[[u,v]]$ has coefficients in $R_0$ although $(F,R_0)$ is not necessarily Landweber exact. We show that the geometric part $X\\mapsto f_0\\mathcal{E}^*(X):=(f_0\\mathcal{E})"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0284","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"}