{"paper":{"title":"Greenberg's $\\mu=0$ conjecture for lisse sheaves over global function fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Anwesh Ray","submitted_at":"2026-07-12T12:25:30Z","abstract_excerpt":"Let $K$ be a global function field of characteristic $p>0$ and $\\ell\\neq p$ be a prime number. We study Selmer groups over a $\\mathbb{Z}_\\ell$-extension $K_\\infty/K$. For a lisse $\\mathbb Z_\\ell$-sheaf we prove that the Pontryagin dual of the associated Selmer group is a finitely generated torsion module over the Iwasawa algebra and has $\\mu$-invariant equal to zero. This gives a positive-characteristic, prime to $p$, analogue of Greenberg's $\\mu=0$ conjecture. Our result applies in particular to abelian varieties, fine Selmer groups, and adjoint representations. We also prove an analogue of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10728","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.10728/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"}