{"paper":{"title":"Lie algebroid Connections, Moduli of $\\mathcal{L}$--twisted Principal Objects and motives","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Arjun Paul, Samit Ghosh","submitted_at":"2026-05-18T12:21:55Z","abstract_excerpt":"Let \\(X\\) be an irreducible smooth complex projective variety, and let \\(G\\) be a connected reductive linear algebraic group over \\(\\mathbb{C}\\). In this paper, we first classify integrable transitive algebraic Lie algebroids on $X$. We then introduce Higgs bundles associated to a Lie algebroid and study their moduli spaces. In particular, we show that the category of vector bundles equipped with integrable \\(\\mathcal{L}\\)-connections and the category of \\(\\mathcal{L}\\)-twisted Higgs bundles of semiharmonic type on \\(X\\) are neutral Tannakian categories, provided that \\(\\mathcal{L}\\) is a tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18304","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/2605.18304/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.207451Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T23:21:58.893944Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1e593c43e8038b40a8c164ae23cf22ef6fdcade8f643f84be73829e3f463b043"},"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"}