{"paper":{"title":"Beilinson-Parshin adeles via solid algebraic geometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christopher Brav, Grigorii Konovalov","submitted_at":"2024-03-13T12:38:09Z","abstract_excerpt":"In this paper, we apply Clausen-Scholze's theory of solid modules to the existence of adelic decompositions for schemes of finite type over $\\mathbb{Z}$. Specifically, we use the six-functor formalism for solid modules to define the skeletal filtration of a scheme, and then we show that decomposing a quasi-coherent sheaf with respect to this filtration gives rise to a new construction of the Beilinson-Parshin adelic resolution. As an application of the adelic decomposition combined with some nice completeness properties of the solid tensor product, we prove a version of adelic descent for soli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.08472","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.08472/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}