{"paper":{"title":"Multivariate $p$-adic formal congruences and integrality of Taylor coefficients of mirror maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG"],"primary_cat":"math.NT","authors_text":"Christian Krattenthaler (Universit\\\"at Wien), Tanguy Rivoal (CNRS et Universit\\'e Grenoble 1)","submitted_at":"2008-04-18T15:57:15Z","abstract_excerpt":"We generalise Dwork's theory of $p$-adic formal congruences from the univariate to a multi-variate setting. We apply our results to prove integrality assertions on the Taylor coefficients of (multi-variable) mirror maps. More precisely, with $\\mathbf z=(z_1,z_2,...,z_d)$, we show that the Taylor coefficients of the multi-variable series $q(\\mathbf z)=z_i\\exp(G(\\mathbf z)/F(\\mathbf z))$ are integers, where $F(\\mathbf z)$ and $G(\\mathbf z)+\\log(z_i) F(\\mathbf z)$, $i=1,2,...,d$, are specific solutions of certain GKZ systems. This result implies the integrality of the Taylor coefficients of numer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.3049","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"}