{"paper":{"title":"Spherical Twists for Gorenstein Orders and $G$-Hilb","license":"http://creativecommons.org/licenses/by/4.0/","headline":"For Gorenstein orders A with suitable quotients B, twists around derived restriction of scalars are autoequivalences whose cotwist is a Nakayama shift.","cross_cats":[],"primary_cat":"math.RT","authors_text":"Marina Godinho","submitted_at":"2026-05-14T14:10:57Z","abstract_excerpt":"This paper constructs derived autoequivalences of Gorenstein orders as twists around spherical functors. More precisely, given a Gorenstein order $A$ and a quotient $p \\colon A \\to B$, then we specify natural conditions on $B$ under which the twist around the corresponding derived restriction of scalars functor is a derived autoequivalence of $A$. In the process, we show that the associated cotwist is a shift of the Nakayama functor of $B$. These results, together with local-to-global technology, are then used construct new derived autoequivalences for skew group algebras and $G$-Hilbert schem"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Given a Gorenstein order A and a quotient p: A → B, under natural conditions on B the twist around the corresponding derived restriction of scalars functor is a derived autoequivalence of A; the associated cotwist is a shift of the Nakayama functor of B.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The natural conditions on the quotient B that make the twist a derived autoequivalence; these are not fully specified in the abstract but are required for the construction to hold.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Constructs derived autoequivalences of Gorenstein orders as spherical twists around derived restriction functors and applies the results to G-Hilbert schemes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"For Gorenstein orders A with suitable quotients B, twists around derived restriction of scalars are autoequivalences whose cotwist is a Nakayama shift.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ad7db9e3af7549234ebf5d01768aaa6fe9df0597ddb9c97586a4eadbcaa8947a"},"source":{"id":"2605.14864","kind":"arxiv","version":1},"verdict":{"id":"be7a674b-45ad-420a-a866-329732d213cd","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T03:16:45.958569Z","strongest_claim":"Given a Gorenstein order A and a quotient p: A → B, under natural conditions on B the twist around the corresponding derived restriction of scalars functor is a derived autoequivalence of A; the associated cotwist is a shift of the Nakayama functor of B.","one_line_summary":"Constructs derived autoequivalences of Gorenstein orders as spherical twists around derived restriction functors and applies the results to G-Hilbert schemes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The natural conditions on the quotient B that make the twist a derived autoequivalence; these are not fully specified in the abstract but are required for the construction to hold.","pith_extraction_headline":"For Gorenstein orders A with suitable quotients B, twists around derived restriction of scalars are autoequivalences whose cotwist is a Nakayama shift."},"references":{"count":13,"sample":[{"doi":"","year":2016,"title":"[Add16] N. Addington. New derived symmetries ofsomehyperkähler varieties.Algebr. Geom.3.2 (2016), pp. 223–260. [AL17] R. Anno and T. Logvinenko. Spherical DG-functors. J. Eur. Math. Soc. (JEMS)19.9 (2","work_id":"c92a4393-cbc1-4927-81dd-4d9febbda0cf","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Spherical functors","work_id":"c4eaa467-a50b-4469-a49f-ca74b5bc7c30","ref_index":2,"cited_arxiv_id":"0711.4409","is_internal_anchor":true},{"doi":"","year":1993,"title":"Cambridge University Press, Cambridge, 1993, pp","work_id":"b5e10616-30f8-45e0-b572-1c7f99fc1493","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2007,"title":"[CMT07] A. Craw, D. Maclagan and R. R. Thomas. Moduli of McKay quiver representations. II. Gröbner basis techniques.J. Algebra316.2 (2007), pp. 514–535. [Don24] W. Donovan. Derived symmetries for crep","work_id":"5ec08ac2-e94c-4b6e-bba3-e5370265c8d8","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"(arXiv : 2409.19555 [math.AG]). [DW16] W. Donovan and M. Wemyss. Noncommutative deformations and flops. Duke Math. J.165.8 (2016), pp. 1397–1474. [DW19a] W. Donovan and M. Wemyss. Contractions and def","work_id":"fcedf456-0102-416c-9a9f-f492c89f2db3","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":13,"snapshot_sha256":"2ff8018bc160629032abb74c732c32ae1b6dcfaf37bb7f75aabfae744b203e4a","internal_anchors":2},"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"}