{"paper":{"title":"Explicit class field theory and the algebraic geometry of $\\Lambda$-rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.KT"],"primary_cat":"math.NT","authors_text":"Bart de Smit, James Borger","submitted_at":"2018-09-07T03:29:13Z","abstract_excerpt":"We consider generalized $\\Lambda$-structures on algebras and schemes over the ring of integers $\\mathit{O}_K$ of a number field $K$. When $K=\\mathbb{Q}$, these agree with the $\\lambda$-ring structures of algebraic K-theory. We then study reduced finite flat $\\Lambda$-rings over $\\mathit{O}_K$ and show that the maximal ones are classified in a Galois theoretic manner by the ray class monoid of Deligne and Ribet. Second, we show that the periodic loci on any $\\Lambda$-scheme of finite type over $\\mathit{O}_K$ generate a canonical family of abelian extensions of $K$. This raises the possibility t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02295","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"}