{"paper":{"title":"Filtration Relative, l'Id\\'eal de Bernstein et ses pentes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Philippe Maisonobe","submitted_at":"2016-10-06T14:24:31Z","abstract_excerpt":"Let $ f_i: X \\rightarrow {\\bf C}$, for $i$ integer between $ 1$ and $ p $, be analytic functions defined on a complex analytic variety $X$. Let us consider $ {\\cal D}_X $ the ring of linear differential operators and $ {\\cal D}_X [s_1, \\ldots, s_p] = {\\bf C}_X [s_1, \\ldots, s_p] \\otimes_ {\\bf C} {\\cal D}_X$. Let $ m $ be a section of a holonomic $ {\\cal D}_X $-Module. We denote $ {\\cal B}(m, x_0, f_1, \\ldots, f_p) $ the ideal of $ { \\bf C} [s_1, \\ldots, s_p] $ constituted by the polynomials $ b $ satisfying in the neighborhood of $ x_0 \\in X$ : $$ B (s_1, \\ldots, s_p) m f_1^{ s_1} \\ldots f_p ^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03354","kind":"arxiv","version":1},"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"}