{"paper":{"title":"AdS Solutions in Gauge Supergravities and the Global Anomaly for the Product of Complex Two-Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"A. A. Bytsenko, E. Elizalde","submitted_at":"2011-05-02T12:27:34Z","abstract_excerpt":"Cohomological methods are applied for the special set of solutions corresponding to rotating branes in arbitrary dimensions, AdS black holes (which can be embedded in ten or eleven dimensions), and gauge supergravities. A new class of solutions is proposed, the Hilbert modular varieties, which consist of the $2n$-fold product of the two-spaces ${\\bf H}^n/\\Gamma$ (where ${\\bf H}^n$ denotes the product of $n$ upper half-planes, $H^2$, equipped with the co-compact action of $\\Gamma \\subset SL(2, {\\mathbb R})^n$) and $({\\bf H}^n)^*/\\Gamma$ (where $(H^2)^* = H^2\\cup \\{{\\rm cusp\\,\\, of}\\,\\,\\Gamma\\}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0309","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"}