{"paper":{"title":"Hodge theory and $G_4$ fluxes in weighted projective spaces: Galois action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Daniel L\\'opez Garcia, Hugo Fortin","submitted_at":"2026-06-04T00:21:16Z","abstract_excerpt":"We extend the explicit study of $G_4$-fluxes and general Hodge cycles from the ordinary Fermat sextic fourfold to tame Fermat-type hypersurfaces in weighted projective space. The main new feature in the weighted setting is that the Galois action on the cyclotomic period data need not preserve the $(2,2)$-subspace. As a consequence, the rational reconstruction of an integral self-dual class can involve additional middle-cohomology components, increasing the norm of the corresponding flux.\n  We work at maximally symmetric Fermat points, where the period matrices and symmetry-invariant Hodge loci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05530","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.05530/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}