{"paper":{"title":"Motivic unipotent fundamental groupoid of $\\mathbb{G}_{m} \\setminus \\mu_{N}$ for $N=2,3,4,6,8$ and Galois descents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Claire Glanois","submitted_at":"2014-11-18T18:11:43Z","abstract_excerpt":"We study Galois descents for categories of mixed Tate motives over $\\mathcal{O}_{N}[1/N]$, for $N\\in \\left\\{2, 3, 4, 8\\right\\}$ or $\\mathcal{O}_{N}$ for $N=6$, with $\\mathcal{O}_{N}$ the ring of integers of the $N^{\\text{th}}$ cyclotomic field, and construct families of motivic iterated integrals with prescribed properties. In particular this gives a basis of honorary multiple zeta values (linear combinations of iterated integrals at roots of unity $\\mu_{N}$ which are multiple zeta values). It also gives a new proof, via Goncharov's coproduct, of Deligne's results: the category of mixed Tate m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4947","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"}