{"paper":{"title":"Semistable Higgs bundles and representations of algebraic fundamental groups: Positive characteristic case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Guitang Lan, Kang Zuo, Mao Sheng","submitted_at":"2012-10-31T10:03:28Z","abstract_excerpt":"Let $k$ be an algebraic closure of finite fields with odd characteristic $p$ and a smooth projective scheme $\\mathbf{X}/W(k)$. Let $\\mathbf{X}^0$ be its generic fiber and $X$ the closed fiber. For $\\mathbf{X}^0$ a curve Faltings conjectured that semistable Higgs bundles of slope zero over $\\mathbf{X}^0_{\\mathbb{C}_p}$ correspond to genuine representations of the algebraic fundamental group of $\\mathbf{X}^0_{\\mathbb{C}_p}$ in his $p$-adic Simpson correspondence. This paper intends to study the conjecture in the characteristic $p$ setting. Among other results, we show that isomorphism classes of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8280","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":""},"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"}