{"paper":{"title":"An explicit theory of $\\pi_{1}^\\mathrm{un,crys}(\\mathbb{P}^{1} - \\{0,\\mu_{N},\\infty\\})$ - II-3 : Sequences of multiple harmonic sums viewed as periods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Jarossay","submitted_at":"2016-01-06T12:38:39Z","abstract_excerpt":"Let $X=\\text{ }\\mathbb{P}^{1} - (\\{0,\\infty\\} \\cup \\mu_{N})\\text{ }/\\text{ }W(\\mathbb{F}_{q})$, with $N \\in \\mathbb{N}^{\\ast}$ and $\\mathbb{F}_{q}$ of characteristic $p$ prime to $N$ and containing a primitive $N$-th root of unity. We establish an explicit theory of the crystalline Frobenius of the pro-unipotent fundamental groupoid of $X$. In part I, we have computed explicitly the Frobenius action. In part II, we use this computation to understand explicitly the algebraic relations of cyclotomic $p$-adic multiple zeta values. We have used the ideas and the vocabulary of the Galois theory of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01159","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"}