{"paper":{"title":"The Fixed Point Locus of the Verschiebung on M_x(2,0) for Genus-2 Curves X in Charateristic 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yanhong Yang","submitted_at":"2011-11-25T03:32:31Z","abstract_excerpt":"In this note, we prove that for every ordinary genus-2 curve $X$ over a finite field $\\kappa$ of characteristic 2 with $\\text{Aut}(X/\\kappa)=\\db{Z}/2\\db{Z} \\times S_3$, there exist $\\text{SL}(2,\\kappa\\sembrack{s})$-representations of $\\pi_1(X)$ such that the image of $\\pi_1(\\bar{X})$ is infinite. This result gives a geometric interpretation of Laszlo's counterexample [12] to a question regarding the finiteness of the geometric monodromy of representations of the fundamental group [4]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5887","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"}