@misc{GLR,
  author = {Gaitsgory, Dennis and Lafforgue, Vincent and Raskin, Sam},
  title = {Tempered vs generic automorphic functions and the canonical filtration on automorphic functions},
  year = {2026},
  eprint = {2603.26925v2},
  archivePrefix = {arXiv},
  primaryClass = {math.NT},
  url = {https://arxiv.org/pdf/2603.26925v2},
  note = {Version 2; author list as on the PDF title page}
}

@misc{ArthurRationality,
  author = {{OpenAI}},
  title = {{Rationality of the Canonical Unramified Arthur Filtration}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Rationality-of-the-Canonical-Unramified-Arthur-Filtration-September-24-2026/paper.pdf}{OAI:Rationality-of-the-Canonical-Unramified-Arthur-Filtration-September-24-2026}},
  year = {2026}
}

@misc{VLafforgue,
  author = {Lafforgue, Vincent},
  title = {Introduction to chtoucas for reductive groups and to the global {Langlands} parameterization},
  year = {2017},
  eprint = {1404.6416v4},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/pdf/1404.6416v4},
  note = {Version 4, 24 December 2017; first posted in 2014}
}

@article{LLafforgue,
  author = {Lafforgue, Laurent},
  title = {Chtoucas de {Drinfeld} et correspondance de {Langlands}},
  journal = {Inventiones Mathematicae},
  volume = {147},
  number = {1},
  year = {2002},
  pages = {1--241},
  doi = {10.1007/s002220100174},
  url = {https://www.laurentlafforgue.org/math/fulltext.pdf}
}

@article{DeligneII,
  author = {Deligne, Pierre},
  title = {La conjecture de {Weil}. {II}},
  journal = {Publications Math{\'e}matiques de l'IH{\'E}S},
  volume = {52},
  year = {1980},
  pages = {137--252},
  doi = {10.1007/BF02684780},
  url = {https://www.numdam.org/item/PMIHES_1980__52__137_0.pdf}
}

@article{MV,
  author = {Mirkovi{\'c}, Ivan and Vilonen, Kari},
  title = {Geometric {Langlands} duality and representations of algebraic groups over commutative rings},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {166},
  number = {1},
  year = {2007},
  pages = {95--143},
  doi = {10.4007/annals.2007.166.95},
  url = {https://annals.math.princeton.edu/2007/166-1/p03}
}

@article{BF,
  author = {Bezrukavnikov, Roman and Finkelberg, Michael},
  title = {Equivariant {Satake} category and {Kostant--Whittaker} reduction},
  journal = {Moscow Mathematical Journal},
  volume = {8},
  number = {1},
  year = {2008},
  pages = {39--72},
  doi = {10.17323/1609-4514-2008-8-1-39-72},
  eprint = {0707.3799v4},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/0707.3799v4},
  note = {Theorem and section locators refer to the corrected arXiv version 4, 9 September 2026}
}

@article{GaitsgoryCentral,
  author = {Gaitsgory, Dennis},
  title = {Construction of central elements in the affine {Hecke} algebra via nearby cycles},
  journal = {Inventiones Mathematicae},
  volume = {144},
  number = {2},
  year = {2001},
  pages = {253--280},
  doi = {10.1007/s002220100122},
  eprint = {math/9912074v4},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/math/9912074v4}
}

@article{AB,
  author = {Arkhipov, Sergey and Bezrukavnikov, Roman},
  title = {Perverse sheaves on affine flags and {Langlands} dual group},
  journal = {Israel Journal of Mathematics},
  volume = {170},
  year = {2009},
  pages = {135--183},
  doi = {10.1007/s11856-009-0024-y},
  eprint = {math/0201073v6},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/math/0201073v6},
  note = {With an appendix by Roman Bezrukavnikov and Ivan Mirkovi{\'c}; locators refer to arXiv version 6}
}

@article{ABG,
  author = {Arkhipov, Sergey and Bezrukavnikov, Roman and Ginzburg, Victor},
  title = {Quantum groups, the loop {Grassmannian}, and the {Springer} resolution},
  journal = {Journal of the American Mathematical Society},
  volume = {17},
  number = {3},
  year = {2004},
  pages = {595--678},
  doi = {10.1090/S0894-0347-04-00454-0},
  eprint = {math/0304173v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/math/0304173v3}
}

@article{BFN,
  author = {Ben-Zvi, David and Francis, John and Nadler, David},
  title = {Integral transforms and {Drinfeld} centers in derived algebraic geometry},
  journal = {Journal of the American Mathematical Society},
  volume = {23},
  number = {4},
  year = {2010},
  pages = {909--966},
  doi = {10.1090/S0894-0347-10-00669-7},
  eprint = {0805.0157v5},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/0805.0157v5}
}

@misc{BZSV,
  author = {Ben-Zvi, David and Sakellaridis, Yiannis and Venkatesh, Akshay},
  title = {Relative {Langlands} duality},
  year = {2024},
  eprint = {2409.04677v1},
  archivePrefix = {arXiv},
  primaryClass = {math.RT},
  url = {https://arxiv.org/pdf/2409.04677v1},
  note = {Version 1; Theorems 6.6.1 and 6.7.5}
}

@article{RicharzScholbach,
  author = {Richarz, Timo and Scholbach, Jakob},
  title = {The motivic {Satake} equivalence},
  journal = {Mathematische Annalen},
  volume = {380},
  year = {2021},
  pages = {1595--1653},
  doi = {10.1007/s00208-021-02176-9},
  url = {https://link.springer.com/article/10.1007/s00208-021-02176-9}
}

@article{EberhardtScholbach,
  author = {Eberhardt, Jens Niklas and Scholbach, Jakob},
  title = {Integral motivic sheaves and geometric representation theory},
  journal = {Advances in Mathematics},
  volume = {412},
  year = {2023},
  pages = {108811},
  doi = {10.1016/j.aim.2022.108811},
  eprint = {2202.11477v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/2202.11477v2},
  note = {Locators refer to arXiv version 2}
}

@misc{CvdHS,
  author = {Cass, Robert and van den Hove, Thibaud and Scholbach, Jakob},
  title = {Central motives on parahoric flag varieties},
  year = {2025},
  eprint = {2403.11007v2},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/pdf/2403.11007v2},
  note = {Version 2; to appear in Journal of the European Mathematical Society}
}

@misc{LiuZheng,
  author = {Liu, Yifeng and Zheng, Weizhe},
  title = {Enhanced six operations and base change theorem for higher {Artin} stacks},
  year = {2024},
  eprint = {1211.5948v4},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/pdf/1211.5948v4},
  note = {Version 4, 17 December 2024; first posted in 2012}
}

@article{LuZheng,
  author = {Lu, Qing and Zheng, Weizhe},
  title = {Categorical traces and a relative {Lefschetz--Verdier} formula},
  journal = {Forum of Mathematics, Sigma},
  volume = {10},
  year = {2022},
  pages = {e10},
  doi = {10.1017/fms.2022.2},
  url = {https://doi.org/10.1017/fms.2022.2}
}

@article{Schieder,
  author = {Schieder, Simon},
  title = {The {Harder--Narasimhan} stratification of the moduli stack of {$G$}-bundles via {Drinfeld}'s compactifications},
  journal = {Selecta Mathematica. New Series},
  volume = {21},
  year = {2015},
  pages = {763--831},
  doi = {10.1007/s00029-014-0161-y},
  eprint = {1212.6814v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/1212.6814v2},
  note = {Theorem and section locators refer to arXiv version 2}
}

@incollection{BeilinsonPerverse,
  author = {Beilinson, A. A.},
  title = {On the derived category of perverse sheaves},
  booktitle = {{$K$}-Theory, Arithmetic and Geometry},
  editor = {Manin, Y. I.},
  series = {Lecture Notes in Mathematics},
  volume = {1289},
  publisher = {Springer},
  address = {Berlin},
  year = {1987},
  pages = {27--41},
  doi = {10.1007/BFb0078365},
  url = {https://www.math.ias.edu/~bhatt/teaching/mat731f15/Beilinson.pdf}
}

@article{SunStacks,
  author = {Sun, Shenghao},
  title = {{$L$}-series of {Artin} stacks over finite fields},
  journal = {Algebra \& Number Theory},
  volume = {6},
  number = {1},
  year = {2012},
  pages = {47--122},
  doi = {10.2140/ant.2012.6.47},
  url = {https://msp.org/ant/2012/6-1/ant-v6-n1-p03-p.pdf}
}

@article{Varshavsky,
  author = {Varshavsky, Yakov},
  title = {{Lefschetz--Verdier} trace formula and a generalization of a theorem of {Fujiwara}},
  journal = {Geometric and Functional Analysis},
  volume = {17},
  year = {2007},
  pages = {271--319},
  doi = {10.1007/s00039-007-0596-9},
  eprint = {math/0505564v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/math/0505564v2}
}

@article{Ram,
  author = {Ram, Arun},
  title = {Affine {Hecke} algebras and generalized standard {Young} tableaux},
  journal = {Journal of Algebra},
  volume = {260},
  number = {1},
  year = {2003},
  pages = {367--415},
  doi = {10.1016/S0021-8693(02)00663-4},
  eprint = {math/0401329v2},
  archivePrefix = {arXiv},
  url = {https://math.soimeme.org/~arunram/Preprints/0401329v2.pdf},
  note = {Theorem and proposition locators refer to the author's arXiv version 2}
}

@book{MW,
  author = {M{\oe}glin, Colette and Waldspurger, Jean-Loup},
  title = {Spectral Decomposition and {Eisenstein} Series: A Paraphrase of the Scriptures},
  series = {Cambridge Tracts in Mathematics},
  volume = {113},
  publisher = {Cambridge University Press},
  address = {Cambridge},
  year = {1995},
  doi = {10.1017/CBO9780511470905},
  url = {https://doi.org/10.1017/CBO9780511470905}
}

@misc{LLafforgueSpectral,
  author = {Lafforgue, Laurent},
  title = {Noyaux du transfert automorphe de {Langlands} et formules de {Poisson} non lin{\'e}aires},
  year = {2013},
  howpublished = {Author's lecture notes},
  url = {https://www.laurentlafforgue.org/math/COURS2013.pdf},
  note = {Theorem III.7, printed p.~36; preparatory definitions on pp.~33--35}
}

@article{MorrisI,
  author = {Morris, L. E.},
  title = {{Eisenstein} series for reductive groups over global function fields. {I}: The cusp form case},
  journal = {Canadian Journal of Mathematics},
  volume = {34},
  number = {1},
  year = {1982},
  pages = {91--168},
  doi = {10.4153/CJM-1982-009-2},
  url = {https://doi.org/10.4153/CJM-1982-009-2}
}

@article{MorrisII,
  author = {Morris, L. E.},
  title = {{Eisenstein} series for reductive groups over global function fields. {II}: The general case},
  journal = {Canadian Journal of Mathematics},
  volume = {34},
  number = {5},
  year = {1982},
  pages = {1112--1182},
  doi = {10.4153/CJM-1982-080-6},
  url = {https://doi.org/10.4153/CJM-1982-080-6}
}

@article{Lang,
  author = {Lang, Serge},
  title = {Algebraic groups over finite fields},
  journal = {American Journal of Mathematics},
  volume = {78},
  number = {3},
  year = {1956},
  pages = {555--563},
  doi = {10.2307/2372673},
  url = {https://wstein.org/papers/bib/Lang-Algebraic_Groups_Over_Finite_Fields.pdf}
}

@incollection{ConradReductive,
  author = {Conrad, Brian},
  title = {Reductive group schemes},
  booktitle = {Autour des sch{\'e}mas en groupes. {Vol. I}},
  series = {Panoramas et Synth{\`e}ses},
  volume = {42/43},
  publisher = {Soci{\'e}t{\'e} Math{\'e}matique de France},
  address = {Paris},
  year = {2014},
  pages = {93--444},
  url = {https://math.stanford.edu/~conrad/papers/luminysga3smf.pdf},
  note = {Locators refer to the author's separately paginated version}
}

@incollection{HoffmannBundles,
  author = {Hoffmann, Norbert},
  title = {On moduli stacks of {$G$}-bundles over a curve},
  editor = {Schmitt, Alexander H. W.},
  booktitle = {Affine Flag Manifolds and Principal Bundles},
  series = {Trends in Mathematics},
  publisher = {Birkh{\"a}user},
  address = {Basel},
  year = {2010},
  pages = {155--163},
  doi = {10.1007/978-3-0346-0288-4_5},
  url = {https://www.maths.mic.ul.ie/hoffmann/pi0.pdf},
  note = {Locators refer to the author's version}
}

@misc{GinzburgLoop,
  author = {Ginzburg, Victor},
  title = {Perverse sheaves on a loop group and {Langlands}' duality},
  year = {2000},
  eprint = {alg-geom/9511007v4},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/alg-geom/9511007v4},
  note = {First posted 1995; locators refer to version 4}
}

@article{Broer,
  author = {Broer, Bram},
  title = {Line bundles on the cotangent bundle of the flag variety},
  journal = {Inventiones Mathematicae},
  volume = {113},
  year = {1993},
  pages = {1--20},
  doi = {10.1007/BF01244299},
  url = {https://gdz.sub.uni-goettingen.de/download/pdf/PPN356556735_0113/LOG_0007.pdf}
}

@article{LaszloOlssonPerverse,
  author = {Laszlo, Yves and Olsson, Martin},
  title = {Perverse {$t$}-structure on {Artin} stacks},
  journal = {Mathematische Zeitschrift},
  volume = {261},
  number = {4},
  year = {2009},
  pages = {737--748},
  doi = {10.1007/s00209-008-0348-z},
  url = {https://www.cmls.polytechnique.fr/perso/laszlo/articleweb/faisceaux-pervers.pdf},
  note = {Theorem locators refer to the author's version}
}

@article{LaszloOlssonSixII,
  author = {Laszlo, Yves and Olsson, Martin},
  title = {The six operations for sheaves on {Artin} stacks. {II}: Adic coefficients},
  journal = {Publications Math{\'e}matiques de l'IH{\'E}S},
  volume = {107},
  year = {2008},
  pages = {169--210},
  doi = {10.1007/s10240-008-0012-5},
  url = {https://www.numdam.org/article/PMIHES_2008__107__169_0.pdf}
}

@article{BMYJM,
  author = {Bertoloni Meli, Alexander and Imai, Naoki and Youcis, Alex},
  title = {The {Jacobson--Morozov} morphism for {Langlands} parameters in the relative setting},
  journal = {International Mathematics Research Notices},
  volume = {2024},
  number = {6},
  year = {2024},
  pages = {5100--5165},
  doi = {10.1093/imrn/rnad217},
  eprint = {2203.01768v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/2203.01768v3},
  note = {Theorem locators refer to arXiv version 3}
}

@article{PappasZhu,
  author = {Pappas, George and Zhu, Xinwen},
  title = {Local models of {Shimura} varieties and a conjecture of {Kottwitz}},
  journal = {Inventiones Mathematicae},
  volume = {194},
  number = {1},
  year = {2013},
  pages = {147--254},
  doi = {10.1007/s00222-012-0442-z},
  eprint = {1110.5588v4},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/1110.5588v4},
  note = {Section and lemma locators refer to arXiv version 4}
}

@article{CapraceCiobotaru,
  author = {Caprace, Pierre-Emmanuel and Ciobotaru, Corina},
  title = {{Gelfand} pairs and strong transitivity for {Euclidean} buildings},
  journal = {Ergodic Theory and Dynamical Systems},
  volume = {35},
  number = {4},
  year = {2015},
  pages = {1056--1078},
  doi = {10.1017/etds.2013.102},
  eprint = {1304.6210v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/1304.6210v2},
  note = {Lemma locators refer to arXiv version 2}
}

@article{JordanRibetScholl,
  author = {Jordan, Bruce W. and Ribet, Kenneth A. and Scholl, Anthony J.},
  title = {Modular curves and {N{\'e}ron} models of generalized {Jacobians}},
  journal = {Compositio Mathematica},
  volume = {160},
  number = {5},
  year = {2024},
  pages = {945--981},
  doi = {10.1112/S0010437X23007662},
  url = {https://doi.org/10.1112/S0010437X23007662}
}

@article{DCHL,
  author = {de Cataldo, Mark Andrea and Haines, Thomas J. and Li, Li},
  title = {{Frobenius} semisimplicity for convolution morphisms},
  journal = {Mathematische Zeitschrift},
  volume = {289},
  number = {1--2},
  year = {2018},
  pages = {119--169},
  doi = {10.1007/s00209-017-1946-4},
  eprint = {1602.00645v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/1602.00645v3},
  note = {Locators refer to arXiv version 3; see also the errata in \cite[Section~12]{HainesPaving}}
}

@article{HainesPaving,
  author = {Haines, Thomas J.},
  title = {Cellular pavings of fibers of convolution morphisms},
  journal = {{\'E}pijournal de G{\'e}om{\'e}trie Alg{\'e}brique},
  volume = {9},
  year = {2025},
  doi = {10.46298/epiga.2024.12352},
  eprint = {2309.14218v4},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/2309.14218v4},
  note = {Article epiga:12352; section locators refer to arXiv version 4}
}

@article{BernsteinLapid,
  author = {Bernstein, Joseph and Lapid, Erez},
  title = {On the meromorphic continuation of {Eisenstein} series},
  journal = {Journal of the American Mathematical Society},
  volume = {37},
  number = {1},
  year = {2024},
  pages = {187--234},
  doi = {10.1090/jams/1020},
  url = {https://www.math.tau.ac.il/~bernstei/Publication_list/publication_texts/2023-10-15-Eisenstein-series-JAMS.pdf},
  note = {Locators refer to the published author offprint}
}

@article{Arthur1989,
  author = {Arthur, James},
  title = {Unipotent automorphic representations: conjectures},
  journal = {Ast{\'e}risque},
  number = {171--172},
  year = {1989},
  pages = {13--71},
  url = {https://www.numdam.org/item/AST_1989__171-172__13_0/}
}

@article{SawinTemplier,
  author = {Sawin, Will and Templier, Nicolas},
  title = {On the {Ramanujan} conjecture for automorphic forms over function fields {I}. {Geometry}},
  journal = {Journal of the American Mathematical Society},
  volume = {34},
  number = {3},
  year = {2021},
  pages = {653--746},
  doi = {10.1090/jams/968},
  eprint = {1805.12231v4},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/1805.12231v4},
  note = {Theorem locators refer to arXiv version 4, 27 September 2020}
}

@misc{CiubotaruHarris,
  author = {Ciubotaru, Dan and Harris, Michael},
  title = {On the generalized {Ramanujan} and {Arthur} conjectures over function fields},
  year = {2023},
  eprint = {2311.15300v1},
  archivePrefix = {arXiv},
  primaryClass = {math.NT},
  url = {https://arxiv.org/pdf/2311.15300v1},
  note = {Version 1, 26 November 2023; theorem locators refer to this version}
}

@misc{HainesKottwitzPrasad,
  author = {Haines, Thomas J. and Kottwitz, Robert E. and Prasad, Amritanshu},
  title = {{Iwahori--Hecke} algebras},
  year = {2009},
  eprint = {math/0309168v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/math/0309168v3},
  note = {Version 3; locators refer to this version}
}

@misc{PrasadBernstein,
  author = {Prasad, Amritanshu},
  title = {On {Bernstein}'s presentation of {Iwahori--Hecke} algebras and representations of split reductive groups over non-{Archimedean} local fields},
  year = {2005},
  eprint = {math/0504417v1},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/math/0504417v1},
  note = {Theorem and section locators refer to arXiv version 1}
}

@incollection{FlathTensorProducts,
  author = {Flath, Daniel},
  title = {Decomposition of representations into tensor products},
  booktitle = {Automorphic Forms, Representations and {$L$}-Functions},
  editor = {Borel, Armand and Casselman, William},
  series = {Proceedings of Symposia in Pure Mathematics},
  volume = {33},
  number = {1},
  publisher = {American Mathematical Society},
  year = {1979},
  pages = {179--183},
  doi = {10.1090/pspum/033.1/546596}
}

@incollection{TitsReductiveLocal,
  author = {Tits, Jacques},
  title = {Reductive groups over local fields},
  booktitle = {Automorphic Forms, Representations and {$L$}-Functions},
  editor = {Borel, Armand and Casselman, William},
  series = {Proceedings of Symposia in Pure Mathematics},
  volume = {33},
  number = {1},
  publisher = {American Mathematical Society},
  year = {1979},
  pages = {29--69},
  url = {https://gkorpal.github.io/files/Tits1979.pdf}
}

@book{MilneAlgebraicGroups,
  author = {Milne, James S.},
  title = {Algebraic Groups: The Theory of Group Schemes of Finite Type over a Field},
  publisher = {Cambridge University Press},
  year = {2017},
  url = {https://www.jmilne.org/math/Books/iAG2017.pdf}
}

@incollection{LeeAdjointQuotients,
  author = {Lee, Ting-Yu},
  title = {Adjoint quotients of reductive groups},
  booktitle = {Autour des sch{\'e}mas en groupes. Vol. III},
  series = {Panoramas et Synth{\`e}ses},
  volume = {47},
  publisher = {Soci{\'e}t{\'e} Math{\'e}matique de France},
  year = {2015},
  pages = {131--145},
  eprint = {1211.3559v1},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/1211.3559v1},
  note = {Theorem and section locators refer to arXiv version 1}
}

@misc{AdamsTaibiCohomology,
  author = {Adams, Jeffrey and Taibi, Olivier},
  title = {Galois and {Cartan} cohomology of real groups},
  year = {2016},
  eprint = {1611.05956v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/1611.05956v2},
  note = {Theorem locators refer to arXiv version 2}
}

@article{SunComparison,
  author = {Sun, Shenghao},
  title = {Generic base change, {Artin}'s comparison theorem, and the decomposition theorem for complex {Artin} stacks},
  journal = {Journal of Algebraic Geometry},
  volume = {26},
  year = {2017},
  pages = {513--555},
  eprint = {1511.01393v1},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/1511.01393v1},
  note = {Theorem and section locators refer to arXiv version 1}
}

@article{JKLMBaseChange,
  author = {Javanpeykar, Ariyan and Kr{\"a}mer, Thomas and Lehn, Christian and Maculan, Marco},
  title = {The monodromy of families of subvarieties on abelian varieties},
  journal = {Duke Mathematical Journal},
  volume = {174},
  number = {6},
  year = {2025},
  doi = {10.1215/00127094-2024-0053},
  eprint = {2210.05166},
  archivePrefix = {arXiv},
  url = {https://webusers.imj-prg.fr/~marco.maculan/files/papers/monodromy.pdf}
}