Modularity theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Modularity theorem" in English language version.

Last modified: 23:16:55, 10 August 2026 (UTC)

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11quantamagazine.org

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adsabs.harvard.edu (Global: 14^th place; English: 9^th place)

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Ribet 1990. Ribet, Kenneth A. (1990), "On modular representations of Gal(Q/Q) arising from modular forms", Inventiones Mathematicae, 100 (2): 431–476, Bibcode:1990InMat.100..431R, doi:10.1007/BF01231195, hdl:10338.dmlcz/147454, ISSN 0020-9910, MR 1047143, S2CID 120614740
Freitas, Le Hung & Siksek 2015. Freitas, Nuno; Le Hung, Bao V.; Siksek, Samir (2015), "Elliptic curves over real quadratic fields are modular", Inventiones Mathematicae, 201 (1): 159–206, arXiv:1310.7088, Bibcode:2015InMat.201..159F, doi:10.1007/s00222-014-0550-z, ISSN 0020-9910, MR 3359051, S2CID 119132800

ams.org (Global: 434^th place; English: 249^th place)

mathscinet.ams.org

Weil 1967. Weil, André (1967), "Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen", Mathematische Annalen, 168: 149–156, doi:10.1007/BF01361551, ISSN 0025-5831, MR 0207658, S2CID 120553723
Frey 1986. Frey, Gerhard (1986), "Links between stable elliptic curves and certain Diophantine equations", Annales Universitatis Saraviensis. Series Mathematicae, 1 (1): iv+40, ISSN 0933-8268, MR 0853387
Serre 1987. Serre, Jean-Pierre (1987), "Sur les représentations modulaires de degré 2 de Gal(Q/Q)", Duke Mathematical Journal, 54 (1): 179–230, doi:10.1215/S0012-7094-87-05413-5, ISSN 0012-7094, MR 0885783
Ribet 1990. Ribet, Kenneth A. (1990), "On modular representations of Gal(Q/Q) arising from modular forms", Inventiones Mathematicae, 100 (2): 431–476, Bibcode:1990InMat.100..431R, doi:10.1007/BF01231195, hdl:10338.dmlcz/147454, ISSN 0020-9910, MR 1047143, S2CID 120614740
Wiles 1995a; Wiles 1995b. Wiles, Andrew (1995a), "Modular elliptic curves and Fermat's last theorem", Annals of Mathematics, Second Series, 141 (3): 443–551, doi:10.2307/2118559, ISSN 0003-486X, JSTOR 2118559, MR 1333035 Wiles, Andrew (1995b), "Modular forms, elliptic curves, and Fermat's last theorem", Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Basel, Boston, Berlin: Birkhäuser, pp. 243–245, MR 1403925
Diamond 1996. Diamond, Fred (1996), "On deformation rings and Hecke rings", Annals of Mathematics, Second Series, 144 (1): 137–166, doi:10.2307/2118586, ISSN 0003-486X, JSTOR 2118586, MR 1405946
Conrad, Diamond & Taylor 1999. Conrad, Brian; Diamond, Fred; Taylor, Richard (1999), "Modularity of certain potentially Barsotti–Tate Galois representations", Journal of the American Mathematical Society, 12 (2): 521–567, doi:10.1090/S0894-0347-99-00287-8, ISSN 0894-0347, MR 1639612
Breuil et al. 2001. Breuil, Christophe; Conrad, Brian; Diamond, Fred; Taylor, Richard (2001), "On the modularity of elliptic curves over Q: wild 3-adic exercises", Journal of the American Mathematical Society, 14 (4): 843–939, doi:10.1090/S0894-0347-01-00370-8, ISSN 0894-0347, MR 1839918
Freitas, Le Hung & Siksek 2015. Freitas, Nuno; Le Hung, Bao V.; Siksek, Samir (2015), "Elliptic curves over real quadratic fields are modular", Inventiones Mathematicae, 201 (1): 159–206, arXiv:1310.7088, Bibcode:2015InMat.201..159F, doi:10.1007/s00222-014-0550-z, ISSN 0020-9910, MR 3359051, S2CID 119132800
Hellegouarch, Yves (1974). "Points d'ordre 2p^h sur les courbes elliptiques" (PDF). Acta Arithmetica. 26 (3): 253–263. doi:10.4064/aa-26-3-253-263. ISSN 0065-1036. MR 0379507.

ams.org

Lang, Serge (November 1995). "Some History of the Shimura-Taniyama Conjecture" (PDF). Notices of the American Mathematical Society. 42 (11): 1301–1307. Retrieved 2022-11-08.

arxiv.org (Global: 49^th place; English: 31^st place)

Harris, Michael (2020). "Virtues of Priority". arXiv:2003.08242 [math.HO].
Boxer, George; Calegari, Frank; Gee, Toby; Pilloni, Vincent (2025-02-28). "Modularity theorems for abelian surfaces". arXiv:2502.20645 [math.NT].
Freitas, Le Hung & Siksek 2015. Freitas, Nuno; Le Hung, Bao V.; Siksek, Samir (2015), "Elliptic curves over real quadratic fields are modular", Inventiones Mathematicae, 201 (1): 159–206, arXiv:1310.7088, Bibcode:2015InMat.201..159F, doi:10.1007/s00222-014-0550-z, ISSN 0020-9910, MR 3359051, S2CID 119132800

doi.org (Global: 2^nd place; English: 2^nd place)

Weil 1967. Weil, André (1967), "Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen", Mathematische Annalen, 168: 149–156, doi:10.1007/BF01361551, ISSN 0025-5831, MR 0207658, S2CID 120553723
Serre 1987. Serre, Jean-Pierre (1987), "Sur les représentations modulaires de degré 2 de Gal(Q/Q)", Duke Mathematical Journal, 54 (1): 179–230, doi:10.1215/S0012-7094-87-05413-5, ISSN 0012-7094, MR 0885783
Ribet 1990. Ribet, Kenneth A. (1990), "On modular representations of Gal(Q/Q) arising from modular forms", Inventiones Mathematicae, 100 (2): 431–476, Bibcode:1990InMat.100..431R, doi:10.1007/BF01231195, hdl:10338.dmlcz/147454, ISSN 0020-9910, MR 1047143, S2CID 120614740
Wiles 1995a; Wiles 1995b. Wiles, Andrew (1995a), "Modular elliptic curves and Fermat's last theorem", Annals of Mathematics, Second Series, 141 (3): 443–551, doi:10.2307/2118559, ISSN 0003-486X, JSTOR 2118559, MR 1333035 Wiles, Andrew (1995b), "Modular forms, elliptic curves, and Fermat's last theorem", Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Basel, Boston, Berlin: Birkhäuser, pp. 243–245, MR 1403925
Diamond 1996. Diamond, Fred (1996), "On deformation rings and Hecke rings", Annals of Mathematics, Second Series, 144 (1): 137–166, doi:10.2307/2118586, ISSN 0003-486X, JSTOR 2118586, MR 1405946
Conrad, Diamond & Taylor 1999. Conrad, Brian; Diamond, Fred; Taylor, Richard (1999), "Modularity of certain potentially Barsotti–Tate Galois representations", Journal of the American Mathematical Society, 12 (2): 521–567, doi:10.1090/S0894-0347-99-00287-8, ISSN 0894-0347, MR 1639612
Breuil et al. 2001. Breuil, Christophe; Conrad, Brian; Diamond, Fred; Taylor, Richard (2001), "On the modularity of elliptic curves over Q: wild 3-adic exercises", Journal of the American Mathematical Society, 14 (4): 843–939, doi:10.1090/S0894-0347-01-00370-8, ISSN 0894-0347, MR 1839918
Freitas, Le Hung & Siksek 2015. Freitas, Nuno; Le Hung, Bao V.; Siksek, Samir (2015), "Elliptic curves over real quadratic fields are modular", Inventiones Mathematicae, 201 (1): 159–206, arXiv:1310.7088, Bibcode:2015InMat.201..159F, doi:10.1007/s00222-014-0550-z, ISSN 0020-9910, MR 3359051, S2CID 119132800
Zagier, D. (1985). "Modular points, modular curves, modular surfaces and modular forms". Arbeitstagung Bonn 1984. Lecture Notes in Mathematics. Vol. 1111. Springer. pp. 225–248. doi:10.1007/BFb0084592. ISBN 978-3-540-39298-9.
Hellegouarch, Yves (1974). "Points d'ordre 2p^h sur les courbes elliptiques" (PDF). Acta Arithmetica. 26 (3): 253–263. doi:10.4064/aa-26-3-253-263. ISSN 0065-1036. MR 0379507.
See the survey of Ribet, K. (1990b). "From the Taniyama–Shimura conjecture to Fermat's Last Theorem". Annales de la Faculté des Sciences de Toulouse. 11: 116–139. doi:10.5802/afst.698.

hdl.handle.net (Global: 66^th place; English: 34^th place)

Ribet 1990. Ribet, Kenneth A. (1990), "On modular representations of Gal(Q/Q) arising from modular forms", Inventiones Mathematicae, 100 (2): 431–476, Bibcode:1990InMat.100..431R, doi:10.1007/BF01231195, hdl:10338.dmlcz/147454, ISSN 0020-9910, MR 1047143, S2CID 120614740

icm.edu.pl (Global: 1,395^th place; English: 4,083^rd place)

matwbn.icm.edu.pl

Hellegouarch, Yves (1974). "Points d'ordre 2p^h sur les courbes elliptiques" (PDF). Acta Arithmetica. 26 (3): 253–263. doi:10.4064/aa-26-3-253-263. ISSN 0065-1036. MR 0379507.

jstor.org (Global: 23^rd place; English: 15^th place)

Wiles 1995a; Wiles 1995b. Wiles, Andrew (1995a), "Modular elliptic curves and Fermat's last theorem", Annals of Mathematics, Second Series, 141 (3): 443–551, doi:10.2307/2118559, ISSN 0003-486X, JSTOR 2118559, MR 1333035 Wiles, Andrew (1995b), "Modular forms, elliptic curves, and Fermat's last theorem", Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Basel, Boston, Berlin: Birkhäuser, pp. 243–245, MR 1403925
Diamond 1996. Diamond, Fred (1996), "On deformation rings and Hecke rings", Annals of Mathematics, Second Series, 144 (1): 137–166, doi:10.2307/2118586, ISSN 0003-486X, JSTOR 2118586, MR 1405946

lmfdb.org (Global: low place; English: low place)

LMFDB: http://www.lmfdb.org/EllipticCurve/Q/37/a/1

numdam.org (Global: 8,359^th place; English: 6,894^th place)

A synthetic presentation (in French) of the main ideas can be found in this Bourbaki article of Jean-Pierre Serre. For more details see Hellegouarch 2001
See the survey of Ribet, K. (1990b). "From the Taniyama–Shimura conjecture to Fermat's Last Theorem". Annales de la Faculté des Sciences de Toulouse. 11: 116–139. doi:10.5802/afst.698.

oeis.org (Global: 1,188^th place; English: 866^th place)

OEIS: https://oeis.org/A007653

quantamagazine.org (Global: 6,258^th place; English: 4,046^th place)

Howlett, Joseph (2025-06-02). "The Core of Fermat's Last Theorem Just Got Superpowered". Quanta Magazine. Retrieved 2025-08-06.

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Weil 1967. Weil, André (1967), "Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen", Mathematische Annalen, 168: 149–156, doi:10.1007/BF01361551, ISSN 0025-5831, MR 0207658, S2CID 120553723
Ribet 1990. Ribet, Kenneth A. (1990), "On modular representations of Gal(Q/Q) arising from modular forms", Inventiones Mathematicae, 100 (2): 431–476, Bibcode:1990InMat.100..431R, doi:10.1007/BF01231195, hdl:10338.dmlcz/147454, ISSN 0020-9910, MR 1047143, S2CID 120614740
Freitas, Le Hung & Siksek 2015. Freitas, Nuno; Le Hung, Bao V.; Siksek, Samir (2015), "Elliptic curves over real quadratic fields are modular", Inventiones Mathematicae, 201 (1): 159–206, arXiv:1310.7088, Bibcode:2015InMat.201..159F, doi:10.1007/s00222-014-0550-z, ISSN 0020-9910, MR 3359051, S2CID 119132800

worldcat.org (Global: 4^th place; English: 4^th place)

search.worldcat.org

Weil 1967. Weil, André (1967), "Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen", Mathematische Annalen, 168: 149–156, doi:10.1007/BF01361551, ISSN 0025-5831, MR 0207658, S2CID 120553723
Frey 1986. Frey, Gerhard (1986), "Links between stable elliptic curves and certain Diophantine equations", Annales Universitatis Saraviensis. Series Mathematicae, 1 (1): iv+40, ISSN 0933-8268, MR 0853387
Serre 1987. Serre, Jean-Pierre (1987), "Sur les représentations modulaires de degré 2 de Gal(Q/Q)", Duke Mathematical Journal, 54 (1): 179–230, doi:10.1215/S0012-7094-87-05413-5, ISSN 0012-7094, MR 0885783
Ribet 1990. Ribet, Kenneth A. (1990), "On modular representations of Gal(Q/Q) arising from modular forms", Inventiones Mathematicae, 100 (2): 431–476, Bibcode:1990InMat.100..431R, doi:10.1007/BF01231195, hdl:10338.dmlcz/147454, ISSN 0020-9910, MR 1047143, S2CID 120614740
Wiles 1995a; Wiles 1995b. Wiles, Andrew (1995a), "Modular elliptic curves and Fermat's last theorem", Annals of Mathematics, Second Series, 141 (3): 443–551, doi:10.2307/2118559, ISSN 0003-486X, JSTOR 2118559, MR 1333035 Wiles, Andrew (1995b), "Modular forms, elliptic curves, and Fermat's last theorem", Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Basel, Boston, Berlin: Birkhäuser, pp. 243–245, MR 1403925
Diamond 1996. Diamond, Fred (1996), "On deformation rings and Hecke rings", Annals of Mathematics, Second Series, 144 (1): 137–166, doi:10.2307/2118586, ISSN 0003-486X, JSTOR 2118586, MR 1405946
Conrad, Diamond & Taylor 1999. Conrad, Brian; Diamond, Fred; Taylor, Richard (1999), "Modularity of certain potentially Barsotti–Tate Galois representations", Journal of the American Mathematical Society, 12 (2): 521–567, doi:10.1090/S0894-0347-99-00287-8, ISSN 0894-0347, MR 1639612
Breuil et al. 2001. Breuil, Christophe; Conrad, Brian; Diamond, Fred; Taylor, Richard (2001), "On the modularity of elliptic curves over Q: wild 3-adic exercises", Journal of the American Mathematical Society, 14 (4): 843–939, doi:10.1090/S0894-0347-01-00370-8, ISSN 0894-0347, MR 1839918
Freitas, Le Hung & Siksek 2015. Freitas, Nuno; Le Hung, Bao V.; Siksek, Samir (2015), "Elliptic curves over real quadratic fields are modular", Inventiones Mathematicae, 201 (1): 159–206, arXiv:1310.7088, Bibcode:2015InMat.201..159F, doi:10.1007/s00222-014-0550-z, ISSN 0020-9910, MR 3359051, S2CID 119132800
Hellegouarch, Yves (1974). "Points d'ordre 2p^h sur les courbes elliptiques" (PDF). Acta Arithmetica. 26 (3): 253–263. doi:10.4064/aa-26-3-253-263. ISSN 0065-1036. MR 0379507.

Modularity theorem (English Wikipedia)

adsabs.harvard.edu (Global: 14th place; English: 9th place)

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ams.org (Global: 434th place; English: 249th place)

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ams.org

arxiv.org (Global: 49th place; English: 31st place)

doi.org (Global: 2nd place; English: 2nd place)

hdl.handle.net (Global: 66th place; English: 34th place)

icm.edu.pl (Global: 1,395th place; English: 4,083rd place)