@article {ancona2021,
    AUTHOR = {Ancona, Giuseppe},
     TITLE = {Standard conjectures for abelian fourfolds},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {223},
      YEAR = {2021},
    NUMBER = {1},
     PAGES = {149--212}
}


@article {bergeron2016,
    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},
     PAGES = {1--125}
}



@misc{broe2026,
Author = {Matt Broe},
Title = {The {T}ate conjecture for abelian fourfolds over finite fields},
Year = {2026},
note = {arXiv:2608.28651},
}


@article {clozel1999,
    AUTHOR = {Clozel, L.},
     TITLE = {Equivalence num\'erique et \'equivalence cohomologique pour
              les vari\'et\'es ab\'eliennes sur les corps finis},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {150},
      YEAR = {1999},
    NUMBER = {1},
     PAGES = {151--163}
}


@incollection{deligne1982,
  author={Deligne, Pierre},
  title={Hodge cycles on abelian varieties (Notes by {J}.{S}. {M}ilne)},
  booktitle={Hodge cycles, motives, and {S}himura varieties},
  year={1982},
  publisher={Springer-Verlag},
  address={Berlin},
  pages={9--100},
  series={Lecture Notes in Mathematics}
}


@article {hazama2000,
    AUTHOR = {Hazama, Fumio},
     TITLE = {Hodge cycles on abelian varieties of {$S_n$}-type},
   JOURNAL = {J. Algebraic Geom.},
  FJOURNAL = {Journal of Algebraic Geometry},
    VOLUME = {9},
      YEAR = {2000},
    NUMBER = {4},
     PAGES = {711--753}
}

@article {hazama2003,
    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},
    VOLUME = {39},
      YEAR = {2003},
    NUMBER = {4},
     PAGES = {625--655}
}

@misc{hoften2026,
  title={The {H}odge Conjecture for {CM} abelian varieties},
  note={hexagon:2610.00259v2},
  year={2026},
  author={van Hoften,Pol and Sempliner, Jack}
}


@article {kisin2025,
    AUTHOR = {Kisin, Mark and Zhou, Rong},
     TITLE = {Independence of {$\ell$} for {F}robenius conjugacy classes
              attached to abelian varieties},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {202},
      YEAR = {2025},
    NUMBER = {3},
     PAGES = {1077--1156}
}

@misc{kisinZ2025,
Author = {Mark Kisin and Rong Zhou},
Title = {Strongly compatible systems associated to semistable abelian varieties},
Year = {2025},
Note = {arXiv:2505.02165},
}

@incollection {kleiman1968,
    AUTHOR = {Kleiman, S. L.},
     TITLE = {Algebraic cycles and the {W}eil conjectures},
 BOOKTITLE = {Dix expos\'{e}s sur la cohomologie des sch\'{e}mas},
    SERIES = {Adv. Stud. Pure Math.},
    VOLUME = {3},
     PAGES = {359--386},
 PUBLISHER = {North-Holland, Amsterdam},
      YEAR = {1968}
}

@incollection {kleiman1994,
    AUTHOR = {Kleiman, Steven L.},
     TITLE = {The standard conjectures},
 BOOKTITLE = {Motives ({S}eattle, {WA}, 1991)},
    SERIES = {Proc. Sympos. Pure Math.},
    VOLUME = {55, Part 1},
     PAGES = {3--20},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1994}
}

@article {langlands1987,
    AUTHOR = {Langlands, R. P. and Rapoport, M.},
     TITLE = {Shimuravariet\"{a}ten und {G}erben},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {378},
      YEAR = {1987},
     PAGES = {113--220}
}


@article {liu2014,
    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},
    VOLUME = {145},
      YEAR = {2014},
    NUMBER = {1-2},
     PAGES = {1--69}
}

@article {liu2021,
    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}
}



@misc{madapusi2026,
  title={Milne's rationality conjecture via simultaneous lifting of {W}eil classes and endomorphisms},
author={Madapusi, Keerthi},
  note={hexagon:2610.00226v1},
  year={2026}
}

@book {milne1980,
    AUTHOR = {Milne, J. S.},
     TITLE = {\'{E}tale cohomology},
    SERIES = {Princeton Mathematical Series, No. 33},
 PUBLISHER = {Princeton University Press, Princeton, NJ},
      YEAR = {1980},
     PAGES = {xiii+323}
}

@incollection {milne1994a,
    AUTHOR = {Milne, J. S.},
     TITLE = {Motives over finite fields},
 BOOKTITLE = {Motives ({S}eattle, {WA}, 1991)},
    SERIES = {Proc. Sympos. Pure Math.},
    VOLUME = {55, Part 1},
     PAGES = {401--459},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1994}
}

@incollection {milne1994b,
    AUTHOR = {Milne, J. S.},
     TITLE = {Shimura varieties and motives},
 BOOKTITLE = {Motives ({S}eattle, {WA}, 1991)},
    SERIES = {Proc. Sympos. Pure Math.},
    VOLUME = {55, Part 2},
     PAGES = {447--523},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1994}
}

@article {milne1999LC,
    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}
}

@article {milne1999LM,
    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}
}

@article {milne2001,
    AUTHOR = {Milne, J. S.},
     TITLE = {The {T}ate conjecture for certain abelian varieties over
              finite fields},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {100},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {135--166}
}

@article {milne2002,
    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}
}

@misc{milne2007a,
Author = {Milne, J. S.},
Title = {Semisimple Algebraic Groups in Characteristic Zero},
Year = {2007},
note = {arXiv:0705.1348}
}

@article {milne2007b,
    AUTHOR = {Milne, J. S.},
     TITLE = {Quotients of {T}annakian categories},
   JOURNAL = {Theory Appl. Categ.},
  FJOURNAL = {Theory and Applications of Categories},
    VOLUME = {18},
      YEAR = {2007},
     PAGES = {No. 21, 654--664}
}

@article {milne2009,
    AUTHOR = {Milne, J. S.},
     TITLE = {Rational {T}ate classes},
   JOURNAL = {Mosc. Math. J.},
  FJOURNAL = {Moscow Mathematical Journal},
    VOLUME = {9},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {111--141}
}

@misc {milne2013,
    AUTHOR = {Milne, J. S.},
     TITLE = {Shimura varieties and moduli},
      YEAR = {2013},
note = {arXiv:1105:0887. Published with a change of numbering in 
Handbook of moduli. Vol. II, 467--548, Adv. Lect. Math. (ALM), 25,
 Int. Press, Somerville, MA, 2013}
}

@article {milne2015,
    AUTHOR = {Milne, J. S.},
     TITLE = {Addendum to ``{V}alues of zeta functions of varieties over
              finite fields''},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {137},
      YEAR = {2015},
    NUMBER = {6},
     PAGES = {1703--1712}
}

@book {milne2017,
    AUTHOR = {Milne, J. S.},
     TITLE = {Algebraic groups: The theory of group schemes of finite type over a field},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {170},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2017},
     PAGES = {xvi+644}
}

@misc{milne2020,
Author = {Milne, J. S.},
Title = {Algebraic groups as automorphism groups of algebras},
Year = {2020},
note = {arXiv:2012.05708v3}
}

@misc{milne2020b,
Author = {Milne, J. S.},
Title = {Hodge classes on abelian varieties},
Year = {2020},
note = {arXiv:2010.08857}
}

@misc{milneLFF,
Author={Milne, J. S.},
Title={Grothendieck's standard conjecture of {L}efschetz type over finite fields},
Year={2020},
note={arXiv:2011.06563}
}

@misc{milneCMT,
Author = {Milne, J. S.},
Title = {Classification of the {M}umford--{T}ate groups of 
polarizable rational {H}odge structures},
Year = {2020},
note = {arXiv:2012.14063v2}
}

@misc{milneHAV,
Author = {Milne, J. S.},
Title = {Hodge classes on abelian varieties},
Year = {2020},
note = {arXiv:2010.08857}
}

@misc{milneDT,
Author = {Milne, J. S.},
Title = {Descent for Algebraic Schemes},
Year = {2024},
note = {arXiv:2406.05550}
}

@misc{milnehc,
Author = {Milne, J. S.},
Title = {Homological categories},
Year = {2024},
note = {In preparation}
}

@misc{milne2025,
Author = {James S. Milne},
Title = {Abelian motives and {S}himura varieties in nonzero characteristic},
Year = {2025},
note = {arXiv:2508.09972},
}

@book {milne2027,
    AUTHOR = {Milne, J. S.},
     TITLE = {Tannakian categories},
    SERIES = {Cambridge Studies in Advanced Mathematics},
     PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2027},
note={To appear}
}


@incollection {serre1994S,
    AUTHOR = {Serre, Jean-Pierre},
     TITLE = {Propri\'et\'es conjecturales des groupes de {G}alois
              motiviques et des repr\'esentations {$l$}-adiques},
 BOOKTITLE = {Motives ({S}eattle, {WA}, 1991)},
    SERIES = {Proc. Sympos. Pure Math.},
    VOLUME = {55, Part 1},
     PAGES = {377--400},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1994}
}

@book {serre2001,
    AUTHOR = {Serre, Jean-Pierre},
     TITLE = {Expos\'es de s\'eminaires (1950-1999)},
    SERIES = {Documents Math\'ematiques (Paris)},
    VOLUME = {1},
 PUBLISHER = {Soci\'et\'e{} Math\'ematique de France, Paris},
      YEAR = {2001},
     PAGES = {viii+259}
}


@article {zink1983,
    AUTHOR = {Zink, Thomas},
     TITLE = {Isogenieklassen von {P}unkten von {S}himuramannigfaltigkeiten
              mit {W}erten in einem endlichen {K}\"orper},
   JOURNAL = {Math. Nachr.},
  FJOURNAL = {Mathematische Nachrichten},
    VOLUME = {112},
      YEAR = {1983},
     PAGES = {103--124}
}