{"paper":{"title":"Euler systems for Galois deformations and the pseudo-isomorphism class of the dual of fine Selmer groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tatsuya Ohshita","submitted_at":"2017-12-25T15:07:17Z","abstract_excerpt":"In this article, we study the pseudo-isomorphism class of the dual fine Selmer group $X$ attached to a $p$-adic Galois deformation whose deformation ring $\\Lambda$ is isomorphic to the ring of formal power series. By using the \"Kolyvagin system\" arising from a given Euler system $c$, we shall construct ideals $C_i(c)$ of $\\Lambda$, and prove that the ideals $C_i(c)$ approximate the higher Fitting ideals of $X$ under suitable hypothesis. In particular, we shall prove that the ideals $C_i(c)$ arising from the Euler system of Beilinson-Kato elements determine the pseudo-isomorphism classes of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09085","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"}