{"paper":{"title":"Invariant Frobenius lifts and deformation of the Hasse invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Buium","submitted_at":"2018-05-24T12:41:27Z","abstract_excerpt":"We show that the $p$-adic completion of any affine elliptic curve with ordinary reduction possesses Frobenius lifts whose \"normalized\" action on $1$-forms preserves mod $p$ the space of invariant $1$-forms. We next show that, after removing the $2$-torsion sections, the above situation can be \"infinitesimally deformed\" in the sense that the above mod $p$ result has a mod $p^2$ analogue. While the \"eigenvalues\" mod $p$ are given by the reciprocal of the Hasse polynomial, the \"eigenvalues\" mod $p^2$ are given by an appropriate $\\d$-modular function whose reciprocal is a $p$-adic deformation of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09636","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"}