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We prove that the upper indecomposable direct summands of the motives of two anisotropic varieties of flags of right ideals X(d_1,...,d_k;A) and X(d'_1,...,d'_s;A') with coefficients in \\mathbb{F} are isomorphic if and only if the p-adic valuations of gcd(d_1,...,d_k) and gcd(d'_1,..,d'_s) are equal and the classes of the p-primary components A_p and A'_p of A and A' generate the same group in the Brauer group of F. This result leads to a surprising dichotomy between upper motives of a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1101.4581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-24T16:13:48Z","cross_cats_sorted":[],"title_canon_sha256":"2cddd872c9f3138167e93c049aa0d3b63495d6168629d3f62f4e9cbcbbe9a760","abstract_canon_sha256":"9387be48d7bf6775abf2b3965acdd0a48bb306b0c4dd9b689baa6a59c3fd0111"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:10.853707Z","signature_b64":"PFY/cZpJsCz5kQR7FKFoGxJvnqK2Oxip2jNi7CrEY9G51FXwOtF/TPwLjw2qqJrKRuAAmMwh2jpUYj1Z/m7+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a54a63b9eb2d08cce53bef53e0e7c0021923660f07e5c456c319f0ae6178ec5d","last_reissued_at":"2026-05-18T04:31:10.853183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:10.853183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of upper motives of algebraic groups of inner type A_n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Charles De Clercq","submitted_at":"2011-01-24T16:13:48Z","abstract_excerpt":"Let A, A' be two central simple algebras over a field F and \\mathbb{F} be a finite field of characteristic p. 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