@article {BMM,
    AUTHOR = {Bergeron, Nicolas and Millson, John and Moeglin, Colette},
     TITLE = {The {H}odge conjecture and arithmetic quotients of complex
              balls},
   JOURNAL = {Acta Math.},
  FJOURNAL = {Acta Mathematica},
    VOLUME = {216},
      YEAR = {2016},
    NUMBER = {1},
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      ISSN = {0001-5962,1871-2509},
   MRCLASS = {11F75 (11F27 14C30 14G35)},
  MRNUMBER = {3508219},
MRREVIEWER = {Jean\ Raimbault},
       DOI = {10.1007/s11511-016-0136-2},
       URL = {https://doi.org/10.1007/s11511-016-0136-2},
}
@article{GQT,
  author    = {Gan, Wee Teck and Qiu, Yannan and Takeda, Shuichiro},
  title     = {The regularized {Siegel}--{Weil} formula (the second term identity) and the {Rallis} inner product formula},
  journal   = {Inventiones mathematicae},
  volume    = {198},
  number    = {3},
  pages     = {739--831},
  year      = {2014},
  publisher = {Springer-Verlag},
  doi       = {10.1007/s00222-014-0509-0}
}
@article{RPK,
  author  = {Kudla, Stephen S.},
  title   = {Splitting metaplectic covers of dual reductive pairs},
  journal = {Israel Journal of Mathematics},
  volume  = {87},
  number  = {1-3},
  pages   = {361--401},
  year    = {1994},
  doi     = {10.1007/BF02773003},
  url     = {https://doi.org/10.1007/BF02773003}
}

@article {Hazama,
    AUTHOR = {Hazama, Fumio},
     TITLE = {On the general {H}odge conjecture for abelian varieties of
              {CM}-type},
   JOURNAL = {Publ. Res. Inst. Math. Sci.},
  FJOURNAL = {Kyoto University. Research Institute for Mathematical
              Sciences. Publications},
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      YEAR = {2003},
    NUMBER = {4},
     PAGES = {625--655},
      ISSN = {0034-5318,1663-4926},
   MRCLASS = {14C30 (14K22)},
  MRNUMBER = {2025458},
MRREVIEWER = {Federica\ Galluzzi},
       URL = {http://projecteuclid.org/euclid.prims/1145476042},
}
@article{Li,
  author  = {Li, Jian-Shu},
  title   = {Non-vanishing theorems for the cohomology of certain arithmetic quotients},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  volume  = {428},
  year    = {1992},
  pages   = {177--217},
  doi     = {10.1515/crll.1992.428.177},
  url     = {https://doi.org/10.1515/crll.1992.428.177}
}
@article {Liu2,
    AUTHOR = {Liu, Yifeng},
     TITLE = {Relative trace formulae toward {B}essel and {F}ourier-{J}acobi
              periods on unitary groups},
   JOURNAL = {Manuscripta Math.},
  FJOURNAL = {Manuscripta Mathematica},
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  MRNUMBER = {3244725},
MRREVIEWER = {Alexandru\ A.\ Popa},
       DOI = {10.1007/s00229-014-0666-x},
       URL = {https://doi.org/10.1007/s00229-014-0666-x},
}
```
@misc{OAI,
  author = {{OpenAI}},
  title = {{The rational Hodge conjecture for CM abelian varieties}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/The-rational-Hodge-conjecture-for-CM-abelian-varieties-October-6-2026/paper.pdf}{github.com/openai/math/blob/main/preprints/}},
  year = {2026}
}
@misc{Bergeron2,
      title={Produits dans la cohomologie des vari\'et\'es arithm\'etiques : quelques calculs sur les s\'eries th\^eta}, 
      author={N. Bergeron},
      year={2006},
      eprint={math/0612447},
      archivePrefix={arXiv},
      primaryClass={math.NT},
      howpublished={\href{https://arxiv.org/abs/math/0612447}{arxiv 0612447}}, 
}

@article {Pohlmann,
    AUTHOR = {Pohlmann, Henry},
     TITLE = {Algebraic cycles on abelian varieties of complex
              multiplication type},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {88},
      YEAR = {1968},
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      ISSN = {0003-486X},
   MRCLASS = {14.48},
  MRNUMBER = {228500},
MRREVIEWER = {M.\ J.\ Greenberg},
       DOI = {10.2307/1970570},
       URL = {https://doi.org/10.2307/1970570},
}
@misc{gao2025hodgecyclesquadraticrelations,
      title={Hodge cycles and quadratic relations between holomorphic periods on {CM} abelian varieties}, 
      author={Ziyang Gao and Emmanuel Ullmo},
      year={2025},
      eprint={2411.12249},
      archivePrefix={arXiv},
      primaryClass={math.NT},
      doi={https://doi.org/10.1017/S1474748025101291},
      howpublished={\href{https://arxiv.org/abs/2411.12249}{arxiv 2411.12249}}, 
}
@misc{MilneHodgeClasses,
      title={Hodge classes on abelian varieties}, 
      author={James S. Milne},
      year={2020},
      eprint={2010.08857},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      howpublished={\url{https://arxiv.org/abs/2010.08857}}, 
}
@article {MR230336,
    AUTHOR = {Lieberman, David I.},
     TITLE = {Numerical and homological equivalence of algebraic cycles on
              {H}odge manifolds},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {90},
      YEAR = {1968},
     PAGES = {366--374},
      ISSN = {0002-9327,1080-6377},
   MRCLASS = {57.60 (53.00)},
  MRNUMBER = {230336},
MRREVIEWER = {D.\ B.\ Scott},
       DOI = {10.2307/2373533},
       URL = {https://doi.org/10.2307/2373533},
}

@article {Liu,
    AUTHOR = {Liu, Yifeng},
     TITLE = {Fourier-{J}acobi cycles and arithmetic relative trace formula
              (with an appendix by {C}hao {L}i and {Y}ihang {Z}hu)},
      NOTE = {Appendix by Chao Li and Yihang Zhu},
   JOURNAL = {Camb. J. Math.},
  FJOURNAL = {Cambridge Journal of Mathematics},
    VOLUME = {9},
      YEAR = {2021},
    NUMBER = {1},
     PAGES = {1--147},
      ISSN = {2168-0930,2168-0949},
   MRCLASS = {11G18 (11G40 14G40)},
  MRNUMBER = {4325259},
MRREVIEWER = {Yongxiong\ Li},
       DOI = {10.4310/CJM.2021.v9.n1.a1},
       URL = {https://doi.org/10.4310/CJM.2021.v9.n1.a1},
}
@article {ClozelHarrisTaylor,
    AUTHOR = {Clozel, Laurent and Harris, Michael and Taylor, Richard},
     TITLE = {Automorphy for some {$l$}-adic lifts of automorphic mod {$l$}
              {G}alois representations},
   JOURNAL = {Publ. Math. Inst. Hautes \'{E}tudes Sci.},
  FJOURNAL = {Publications Math\'{e}matiques. Institut de Hautes \'{E}tudes
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      YEAR = {2008},
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      ISSN = {0073-8301,1618-1913},
   MRCLASS = {11F80 (11G18 11R34)},
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MRREVIEWER = {Mark\ Kisin},
       DOI = {10.1007/s10240-008-0016-1},
       URL = {https://doi.org/10.1007/s10240-008-0016-1},
}
@article {WedhornOrdinary,
    AUTHOR = {Wedhorn, Torsten},
     TITLE = {Ordinariness in good reductions of {S}himura varieties of
              {PEL}-type},
   JOURNAL = {Ann. Sci. \'{E}cole Norm. Sup. (4)},
  FJOURNAL = {Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure.
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      YEAR = {1999},
    NUMBER = {5},
     PAGES = {575--618},
      ISSN = {0012-9593},
   MRCLASS = {11G18 (14G35 14L05)},
  MRNUMBER = {1710754},
MRREVIEWER = {Ben\ Moonen},
       DOI = {10.1016/S0012-9593(01)80001-X},
       URL = {https://doi.org/10.1016/S0012-9593(01)80001-X},
}
@article {WedhornCongruence,
    AUTHOR = {Wedhorn, Torsten},
     TITLE = {Congruence relations on some {S}himura varieties},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {524},
      YEAR = {2000},
     PAGES = {43--71},
      ISSN = {0075-4102,1435-5345},
   MRCLASS = {11G18 (14G35)},
  MRNUMBER = {1770603},
MRREVIEWER = {Ben\ Moonen},
       DOI = {10.1515/crll.2000.060},
       URL = {https://doi.org/10.1515/crll.2000.060},
}
@incollection {DeligneHodge,
    AUTHOR = {Deligne, Pierre},
     TITLE = {The {H}odge conjecture},
 BOOKTITLE = {The millennium prize problems},
     PAGES = {45--53},
 PUBLISHER = {Clay Math. Inst., Cambridge, MA},
      YEAR = {2006},
      ISBN = {0-8218-3679-X},
   MRCLASS = {14C30 (32J25)},
  MRNUMBER = {2238273},
}
@inproceedings {HodgeHodge,
    AUTHOR = {Hodge, W. V. D.},
     TITLE = {The topological invariants of algebraic varieties},
 BOOKTITLE = {Proceedings of the {I}nternational {C}ongress of
              {M}athematicians, {C}ambridge, {M}ass., 1950, vol. 1},
     PAGES = {182--192},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1952},
   MRCLASS = {14.0X},
  MRNUMBER = {46075},
MRREVIEWER = {P.\ Dolbeault},
}
@misc{markman2025cyclesabelian2nfoldsweil,
      title="{Cycles on abelian 2n-folds of Weil type from secant sheaves on abelian n-folds}", 
      author={Eyal Markman},
      year={2025},
      eprint={2502.03415},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      howpublished={\href{https://arxiv.org/abs/2502.03415}{arxiv 2502.03415}}, 
}

@article {MoonenZarhin,
    AUTHOR = {Moonen, B. J. J. and Zarhin, Yu. G.},
     TITLE = {Hodge classes on abelian varieties of low dimension},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {315},
      YEAR = {1999},
    NUMBER = {4},
     PAGES = {711--733},
      ISSN = {0025-5831,1432-1807},
   MRCLASS = {14C30 (14K22)},
  MRNUMBER = {1731466},
MRREVIEWER = {Fumio\ Hazama},
       DOI = {10.1007/s002080050333},
       URL = {https://doi.org/10.1007/s002080050333},
}

@article {MilneTate,
    AUTHOR = {Milne, J. S.},
     TITLE = {Lefschetz motives and the {T}ate conjecture},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {117},
      YEAR = {1999},
    NUMBER = {1},
     PAGES = {45--76},
      ISSN = {0010-437X,1570-5846},
   MRCLASS = {11G09 (11G10 11G15 14C25 14K15)},
  MRNUMBER = {1692999},
MRREVIEWER = {Ben\ Moonen},
       DOI = {10.1023/A:1000776613765},
       URL = {https://doi.org/10.1023/A:1000776613765},
}
@article {MilneHodgeStandard,
    AUTHOR = {Milne, J. S.},
     TITLE = {Polarizations and {G}rothendieck's standard conjectures},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {155},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {599--610},
      ISSN = {0003-486X,1939-8980},
   MRCLASS = {14C30 (14C25 14K22 14K99)},
  MRNUMBER = {1906596},
MRREVIEWER = {Giuseppe\ Lombardo},
       DOI = {10.2307/3062126},
       URL = {https://doi.org/10.2307/3062126},
}
@misc{MilneCM,
  author = {Milne, J. S.},
  title  = {Complex Multiplication},
  year   = {2020},
  note   = {Course notes, version 0.10, July 14, 2020},
  url    = {https://www.jmilne.org/math/CourseNotes/CM.pdf}
}
@misc{MilneCFT,
  author = {Milne, J. S.},
  title  = {Class Field Theory},
  year   = {2020},
  note   = {Course notes, version 4.03, August 6, 2020},
  url    = {https://www.jmilne.org/math/CourseNotes/CFT.pdf}
}
@article {MoonenZarhinII,
    AUTHOR = {Moonen, B. J. J. and Zarhin, Yu. G.},
     TITLE = {Hodge classes and {T}ate classes on simple abelian fourfolds},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {77},
      YEAR = {1995},
    NUMBER = {3},
     PAGES = {553--581},
      ISSN = {0012-7094,1547-7398},
   MRCLASS = {14C30 (11G10 14K15)},
  MRNUMBER = {1324634},
MRREVIEWER = {Fumio\ Hazama},
       DOI = {10.1215/S0012-7094-95-07717-5},
       URL = {https://doi.org/10.1215/S0012-7094-95-07717-5},
}
@article {Abdulali,
    AUTHOR = {Abdulali, Salman},
     TITLE = {Hodge structures on abelian varieties of type {III}},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {155},
      YEAR = {2002},
    NUMBER = {3},
     PAGES = {915--928},
      ISSN = {0003-486X,1939-8980},
   MRCLASS = {14C30 (14K10)},
  MRNUMBER = {1923969},
MRREVIEWER = {Giuseppe\ Lombardo},
       DOI = {10.2307/3062136},
       URL = {https://doi.org/10.2307/3062136},
}
@misc{gordon1997surveyhodgeconjectureabelian,
      title="{A Survey of the Hodge Conjecture for Abelian Varieties}", 
      author={B. Brent Gordon},
      year={1997},
      eprint={alg-geom/9709030},
      archivePrefix={arXiv},
      primaryClass={alg-geom},
      howpublished ={\url{https://arxiv.org/abs/alg-geom/9709030}}, 
}
@misc{floccari2026hodgeconjectureweilfourfolds,
      title="{The Hodge conjecture for Weil fourfolds with discriminant 1 via singular OG6-varieties}", 
      author={Salvatore Floccari and Lie Fu},
      year={2026},
      eprint={2504.13607},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      howpublished={\href{https://arxiv.org/abs/2504.13607}{arxiv 2504.13607}}, 
}
@article {AbdulaliGHC,
    AUTHOR = {Abdulali, Salman},
     TITLE = {Hodge structures of {CM}-type},
   JOURNAL = {J. Ramanujan Math. Soc.},
  FJOURNAL = {Journal of the Ramanujan Mathematical Society},
    VOLUME = {20},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {155--162},
      ISSN = {0970-1249,2320-3110},
   MRCLASS = {14C30 (14K22)},
  MRNUMBER = {2169094},
MRREVIEWER = {Federica\ Galluzzi},
}
@misc{Milne2008TateConjecture,
  author = {Milne, J. S.},
  title  = {The Tate Conjecture over Finite Fields ({AIM} Talk)},
  year   = {2008},
  note   = {Notes for a talk at the American Institute of Mathematics,
            version 2.2, May 7, 2008},
  howpublished    = {\url{https://www.jmilne.org/math/articles/2007e.pdf}}
}
@article {MilneLefschetzClasses,
    AUTHOR = {Milne, J. S.},
     TITLE = {Lefschetz classes on abelian varieties},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {96},
      YEAR = {1999},
    NUMBER = {3},
     PAGES = {639--675},
      ISSN = {0012-7094,1547-7398},
   MRCLASS = {14C25 (11G10 14C30 14K05)},
  MRNUMBER = {1671217},
MRREVIEWER = {Fumio\ Hazama},
       DOI = {10.1215/S0012-7094-99-09620-5},
       URL = {https://doi.org/10.1215/S0012-7094-99-09620-5},
}
@article {MR2099754,
    AUTHOR = {Koike, Kenji},
     TITLE = {Algebraicity of some {W}eil {H}odge classes},
   JOURNAL = {Canad. Math. Bull.},
  FJOURNAL = {Canadian Mathematical Bulletin. Bulletin Canadien de
              Math\'{e}matiques},
    VOLUME = {47},
      YEAR = {2004},
    NUMBER = {4},
     PAGES = {566--572},
      ISSN = {0008-4395,1496-4287},
   MRCLASS = {14C30 (11G18 14H40)},
  MRNUMBER = {2099754},
MRREVIEWER = {Fumio\ Hazama},
       DOI = {10.4153/CMB-2004-055-x},
       URL = {https://doi.org/10.4153/CMB-2004-055-x},
}
@article {AbdulaliIII,
    AUTHOR = {Abdulali, Salman},
     TITLE = {Hodge structures on abelian varieties of type {IV}},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {246},
      YEAR = {2004},
    NUMBER = {1-2},
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      ISSN = {0025-5874,1432-1823},
   MRCLASS = {14C30 (14K05 14K20)},
  MRNUMBER = {2031453},
MRREVIEWER = {Syoji\ Tsuboi},
       DOI = {10.1007/s00209-003-0595-y},
       URL = {https://doi.org/10.1007/s00209-003-0595-y},
}
@misc{vangeemen2026hyperkahlersixfoldsabelianfourfolds,
      title="{Hyperk\"ahler sixfolds, abelian fourfolds of Weil type and a Hodge class}", 
      author={Bert van Geemen and Antonio Rapagnetta},
      year={2026},
      eprint={2607.18341},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      howpublished={\href{https://arxiv.org/abs/2607.18341}{2607.18341}}, 
}
@article {HazamaIII,
    AUTHOR = {Hazama, Fumio},
     TITLE = {Hodge cycles on abelian varieties with complex multiplication
              by cyclic {CM}-fields},
   JOURNAL = {J. Math. Sci. Univ. Tokyo},
  FJOURNAL = {The University of Tokyo. Journal of Mathematical Sciences},
    VOLUME = {10},
      YEAR = {2003},
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     PAGES = {581--598},
      ISSN = {1340-5705},
   MRCLASS = {14C30 (14K10)},
  MRNUMBER = {2037760},
MRREVIEWER = {Xian\ Wu},
}
@article {HazamaII,
    AUTHOR = {Hazama, Fumio},
     TITLE = {Discrete tomography and the {H}odge conjecture for certain
              abelian varieties of {CM}-type},
   JOURNAL = {Proc. Japan Acad. Ser. A Math. Sci.},
  FJOURNAL = {Japan Academy. Proceedings. Series A. Mathematical Sciences},
    VOLUME = {82},
      YEAR = {2006},
    NUMBER = {3},
     PAGES = {25--29},
      ISSN = {0386-2194},
   MRCLASS = {14C30 (14K05 39A10)},
  MRNUMBER = {2214769},
MRREVIEWER = {Giuseppe\ Lombardo},
       URL = {http://projecteuclid.org/euclid.pja/1144158988},
}
@article {AbdulaliIV,
    AUTHOR = {Abdulali, Salman},
     TITLE = {Abelian varieties of type {III} and the {H}odge conjecture},
   JOURNAL = {Internat. J. Math.},
  FJOURNAL = {International Journal of Mathematics},
    VOLUME = {10},
      YEAR = {1999},
    NUMBER = {6},
     PAGES = {667--675},
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   MRCLASS = {14C30 (14K12 14K15)},
  MRNUMBER = {1715177},
       DOI = {10.1142/S0129167X99000264},
       URL = {https://doi.org/10.1142/S0129167X99000264},
}
@article {AbdulaliV,
    AUTHOR = {Abdulali, Salman},
     TITLE = {Hodge structures on abelian varieties of type {III}},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {155},
      YEAR = {2002},
    NUMBER = {3},
     PAGES = {915--928},
      ISSN = {0003-486X,1939-8980},
   MRCLASS = {14C30 (14K10)},
  MRNUMBER = {1923969},
MRREVIEWER = {Giuseppe\ Lombardo},
       DOI = {10.2307/3062136},
       URL = {https://doi.org/10.2307/3062136},
}

@article {OSullivan,
    AUTHOR = {O'Sullivan, Peter},
     TITLE = {Algebraic cycles on an abelian variety},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {654},
      YEAR = {2011},
     PAGES = {1--81},
      ISSN = {0075-4102,1435-5345},
   MRCLASS = {14C25 (14K05)},
  MRNUMBER = {2795752},
MRREVIEWER = {Fumio\ Hazama},
       DOI = {10.1515/CRELLE.2011.025},
       URL = {https://doi.org/10.1515/CRELLE.2011.025},
}
@article {MR2384535,
    AUTHOR = {Ram\'{o}n Mar\'{\i}, Jos\'{e} J.},
     TITLE = {On the {H}odge conjecture for products of certain surfaces},
   JOURNAL = {Collect. Math.},
  FJOURNAL = {Universitat de Barcelona. Collectanea Mathematica},
    VOLUME = {59},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {1--26},
      ISSN = {0010-0757,2038-4815},
   MRCLASS = {14C30 (14C15 14K99)},
  MRNUMBER = {2384535},
MRREVIEWER = {Federica\ Galluzzi},
       DOI = {10.1007/BF03191179},
       URL = {https://doi.org/10.1007/BF03191179},
}
@misc{Agugliaro2025,
  author = {Thomas Agugliaro},
  title = "{Standard conjecture of {Hodge} type for powers of abelian varieties}",
  year = {2025},
  eprint = {2510.21562},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  howpublished={\href{https://arxiv.org/abs/2510.21562}{arxiv 2510.21562}},
}
@article {MarkmanKummer,
    AUTHOR = {Markman, Eyal},
     TITLE = {The monodromy of generalized {K}ummer varieties and algebraic
              cycles on their intermediate {J}acobians},
   JOURNAL = {J. Eur. Math. Soc. (JEMS)},
  FJOURNAL = {Journal of the European Mathematical Society (JEMS)},
    VOLUME = {25},
      YEAR = {2023},
    NUMBER = {1},
     PAGES = {231--321},
      ISSN = {1435-9855,1435-9863},
   MRCLASS = {14C25 (14C30 14F08 14G05 14J42)},
  MRNUMBER = {4556784},
MRREVIEWER = {Arnaud\ Beauville},
       DOI = {10.4171/jems/1199},
       URL = {https://doi.org/10.4171/jems/1199},
}
@misc{floccari2025k3surfacesassociatedvarieties,
      title="{K3 surfaces associated with varieties of generalized Kummer type}", 
      author={Salvatore Floccari},
      year={2025},
      eprint={2501.02315},
      archivePrefix={arXiv},
      primaryClass={math.AG},
      howpublished={\href{https://arxiv.org/abs/2501.02315}{2501.02315}}, 
}
@misc{markman2026secantsheavesweilclasses,
      title="{Secant sheaves and Weil classes on abelian varieties}", 
      author={Eyal Markman},
      year={2026},
      eprint={2509.23403},
      archivePrefix={arXiv},
      primaryClass={math.AG},
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