[{"day":"27","type":"journal_article","intvolume":"        30","status":"public","publication":"Selecta Mathematica","issue":"2","month":"01","date_published":"2024-01-27T00:00:00Z","article_type":"original","scopus_import":"1","publisher":"Springer Nature","language":[{"iso":"eng"}],"department":[{"_id":"TaHa"}],"date_created":"2024-02-04T23:00:53Z","citation":{"short":"T. Hausel, E. Letellier, F. Rodriguez-Villegas, Selecta Mathematica 30 (2024).","ista":"Hausel T, Letellier E, Rodriguez-Villegas F. 2024. Locally free representations of quivers over commutative Frobenius algebras. Selecta Mathematica. 30(2), 20.","ama":"Hausel T, Letellier E, Rodriguez-Villegas F. Locally free representations of quivers over commutative Frobenius algebras. <i>Selecta Mathematica</i>. 2024;30(2). doi:<a href=\"https://doi.org/10.1007/s00029-023-00914-2\">10.1007/s00029-023-00914-2</a>","mla":"Hausel, Tamás, et al. “Locally Free Representations of Quivers over Commutative Frobenius Algebras.” <i>Selecta Mathematica</i>, vol. 30, no. 2, 20, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00029-023-00914-2\">10.1007/s00029-023-00914-2</a>.","chicago":"Hausel, Tamás, Emmanuel Letellier, and Fernando Rodriguez-Villegas. “Locally Free Representations of Quivers over Commutative Frobenius Algebras.” <i>Selecta Mathematica</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00029-023-00914-2\">https://doi.org/10.1007/s00029-023-00914-2</a>.","ieee":"T. Hausel, E. Letellier, and F. Rodriguez-Villegas, “Locally free representations of quivers over commutative Frobenius algebras,” <i>Selecta Mathematica</i>, vol. 30, no. 2. Springer Nature, 2024.","apa":"Hausel, T., Letellier, E., &#38; Rodriguez-Villegas, F. (2024). Locally free representations of quivers over commutative Frobenius algebras. <i>Selecta Mathematica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00029-023-00914-2\">https://doi.org/10.1007/s00029-023-00914-2</a>"},"publication_status":"epub_ahead","abstract":[{"text":"In this paper we investigate locally free representations of a quiver Q over a commutative Frobenius algebra R by arithmetic Fourier transform. When the base field is finite we prove that the number of isomorphism classes of absolutely indecomposable locally free representations of fixed rank is independent of the orientation of Q. We also prove that the number of isomorphism classes of locally free absolutely indecomposable representations of the preprojective algebra of Q over R equals the number of isomorphism classes of locally free absolutely indecomposable representations of Q over R[t]/(t2). Using these results together with results of Geiss, Leclerc and Schröer we give, when k is algebraically closed, a classification of pairs (Q, R) such that the set of isomorphism classes of indecomposable locally free representations of Q over R is finite. Finally when the representation is free of rank 1 at each vertex of Q, we study the function that counts the number of isomorphism classes of absolutely indecomposable locally free representations of Q over the Frobenius algebra Fq[t]/(tr). We prove that they are polynomial in q and their generating function is rational and satisfies a functional equation.","lang":"eng"}],"author":[{"first_name":"Tamás","full_name":"Hausel, Tamás","last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Letellier","full_name":"Letellier, Emmanuel","first_name":"Emmanuel"},{"first_name":"Fernando","last_name":"Rodriguez-Villegas","full_name":"Rodriguez-Villegas, Fernando"}],"article_processing_charge":"No","volume":30,"date_updated":"2024-02-05T12:58:21Z","publication_identifier":{"issn":["1022-1824"],"eissn":["1420-9020"]},"_id":"14930","oa_version":"None","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"Special thanks go to Christof Geiss, Bernard Leclerc and Jan Schröer for explaining their work but also for sharing some unpublished results with us. We also thank the referee for many useful suggestions. We would like to thank Tommaso Scognamiglio for pointing out a mistake in the proof of Proposition 5.17 in an earlier version of the paper. We would like also to thank Alexander Beilinson, Bill Crawley-Boevey, Joel Kamnitzer, and Peng Shan for useful discussions.","year":"2024","doi":"10.1007/s00029-023-00914-2","title":"Locally free representations of quivers over commutative Frobenius algebras","article_number":"20"},{"title":"On the local-global principle for isogenies of abelian surfaces","external_id":{"arxiv":["2206.15240"]},"year":"2024","doi":"10.1007/s00029-023-00908-0","main_file_link":[{"url":"https://arxiv.org/abs/2206.15240","open_access":"1"}],"article_number":"18","abstract":[{"text":"Let $\\ell$ be a prime number. We classify the subgroups $G$ of $\\operatorname{Sp}_4(\\mathbb{F}_\\ell)$ and $\\operatorname{GSp}_4(\\mathbb{F}_\\ell)$ that act irreducibly on $\\mathbb{F}_\\ell^4$, but such that every element of $G$ fixes an $\\mathbb{F}_\\ell$-vector subspace of dimension 1. We use this classification to prove that the local-global principle for isogenies of degree $\\ell$ between abelian surfaces over number fields holds in many cases -- in particular, whenever the abelian surface has non-trivial endomorphisms and $\\ell$ is large enough with respect to the field of definition. Finally, we prove that there exist arbitrarily large primes $\\ell$ for which some abelian surface\r\n$A/\\mathbb{Q}$ fails the local-global principle for isogenies of degree $\\ell$.","lang":"eng"}],"author":[{"first_name":"Davide","last_name":"Lombardo","full_name":"Lombardo, Davide"},{"id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","first_name":"Matteo","full_name":"Verzobio, Matteo","last_name":"Verzobio","orcid":"0000-0002-0854-0306"}],"publication_status":"epub_ahead","_id":"12312","publication_identifier":{"issn":["4321-1234"],"issnl":["1022-1824"],"eissn":["1420-9020"]},"acknowledgement":"It is a pleasure to thank Samuele Anni for his interest in this project and for several discussions on the topic of this paper, which led in particular to Remark 6.30 and to a better understanding of the difficulties with [6]. We also thank John Cullinan for correspondence about [6] and Barinder Banwait for his many insightful comments on the first version of this paper. Finally, we thank the referee for their thorough reading of the manuscript.\r\nOpen access funding provided by Università di Pisa within the CRUI-CARE Agreement. The authors have been partially supported by MIUR (Italy) through PRIN 2017 “Geometric, algebraic and analytic methods in arithmetic\" and PRIN 2022 “Semiabelian varieties, Galois representations and related Diophantine problems\", and by the University of Pisa through PRA 2018-19 and 2022 “Spazi di moduli, rappresentazioni e strutture combinatorie\". The first author is a member of the INdAM group GNSAGA.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","quality_controlled":"1","arxiv":1,"date_updated":"2025-02-13T11:47:12Z","volume":30,"oa":1,"article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","scopus_import":"1","language":[{"iso":"eng"}],"OA_place":"repository","month":"01","article_type":"original","date_published":"2024-01-26T00:00:00Z","date_created":"2023-01-16T11:45:53Z","department":[{"_id":"TiBr"}],"intvolume":"        30","OA_type":"green","status":"public","day":"26","type":"journal_article","issue":"2","publication":"Selecta Mathematica"},{"department":[{"_id":"TaHa"}],"has_accepted_license":"1","file":[{"file_size":584648,"file_name":"2021_SelectaMath_Koroteev.pdf","checksum":"beadc5a722ffb48190e1e63ee2dbfee5","date_created":"2021-09-13T11:31:34Z","access_level":"open_access","date_updated":"2021-09-13T11:31:34Z","success":1,"relation":"main_file","content_type":"application/pdf","creator":"cchlebak","file_id":"10010"}],"date_created":"2021-09-12T22:01:22Z","date_published":"2021-08-30T00:00:00Z","article_type":"original","month":"08","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Springer Nature","file_date_updated":"2021-09-13T11:31:34Z","publication":"Selecta Mathematica","issue":"5","type":"journal_article","day":"30","status":"public","intvolume":"        27","article_number":"87","isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["530"],"doi":"10.1007/s00029-021-00698-3","year":"2021","title":"Quantum K-theory of quiver varieties and many-body systems","external_id":{"isi":["000692795200001"]},"article_processing_charge":"Yes (via OA deal)","volume":27,"oa":1,"date_updated":"2023-08-14T06:34:14Z","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","oa_version":"Published Version","acknowledgement":"First of all we would like to thank Andrei Okounkov for invaluable discussions, advises and sharing with us his fantastic viewpoint on modern quantum geometry. We are also grateful to D. Korb and Z. Zhou for their interest and comments. The work of A. Smirnov was supported in part by RFBR Grants under Numbers 15-02-04175 and 15-01-04217 and in part by NSF Grant DMS–2054527. The work of P. Koroteev, A.M. Zeitlin and A. Smirnov is supported in part by AMS Simons travel Grant. A. M. Zeitlin is partially supported by Simons Collaboration Grant, Award ID: 578501. Open access funding provided by Institute of Science and Technology (IST Austria).","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"eissn":["1420-9020"],"issn":["1022-1824"]},"_id":"9998","citation":{"ama":"Koroteev P, Pushkar P, Smirnov AV, Zeitlin AM. Quantum K-theory of quiver varieties and many-body systems. <i>Selecta Mathematica</i>. 2021;27(5). doi:<a href=\"https://doi.org/10.1007/s00029-021-00698-3\">10.1007/s00029-021-00698-3</a>","mla":"Koroteev, Peter, et al. “Quantum K-Theory of Quiver Varieties and Many-Body Systems.” <i>Selecta Mathematica</i>, vol. 27, no. 5, 87, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s00029-021-00698-3\">10.1007/s00029-021-00698-3</a>.","short":"P. Koroteev, P. Pushkar, A.V. Smirnov, A.M. Zeitlin, Selecta Mathematica 27 (2021).","ista":"Koroteev P, Pushkar P, Smirnov AV, Zeitlin AM. 2021. Quantum K-theory of quiver varieties and many-body systems. Selecta Mathematica. 27(5), 87.","ieee":"P. Koroteev, P. Pushkar, A. V. Smirnov, and A. M. Zeitlin, “Quantum K-theory of quiver varieties and many-body systems,” <i>Selecta Mathematica</i>, vol. 27, no. 5. Springer Nature, 2021.","apa":"Koroteev, P., Pushkar, P., Smirnov, A. V., &#38; Zeitlin, A. M. (2021). Quantum K-theory of quiver varieties and many-body systems. <i>Selecta Mathematica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00029-021-00698-3\">https://doi.org/10.1007/s00029-021-00698-3</a>","chicago":"Koroteev, Peter, Petr Pushkar, Andrey V. Smirnov, and Anton M. Zeitlin. “Quantum K-Theory of Quiver Varieties and Many-Body Systems.” <i>Selecta Mathematica</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00029-021-00698-3\">https://doi.org/10.1007/s00029-021-00698-3</a>."},"publication_status":"published","author":[{"full_name":"Koroteev, Peter","last_name":"Koroteev","first_name":"Peter"},{"id":"151DCEB6-9EC3-11E9-8480-ABECE5697425","last_name":"Pushkar","full_name":"Pushkar, Petr","first_name":"Petr"},{"last_name":"Smirnov","full_name":"Smirnov, Andrey V.","first_name":"Andrey V."},{"full_name":"Zeitlin, Anton M.","last_name":"Zeitlin","first_name":"Anton M."}],"abstract":[{"text":"We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces a K-theoretic version of results of Givental and Kim, connecting quantum geometry of flag varieties and Toda lattice.","lang":"eng"}]}]