Editing Modularity theorem (section)

==References==
{{reflist|20em}}

=== Bibliography ===
{{refbegin|20em}}
*{{Citation | last1=Breuil | first1=Christophe | last2=Conrad | first2=Brian | last3=Diamond | first3=Fred | last4=Taylor | first4=Richard | title=On the modularity of elliptic curves over '''Q''': wild 3-adic exercises | doi=10.1090/S0894-0347-01-00370-8 | mr=1839918 | year=2001 | journal=[[Journal of the American Mathematical Society]] | issn=0894-0347 | volume=14 | issue=4 | pages=843–939| doi-access=free }}
*{{Citation | last1=Conrad | first1=Brian | last2=Diamond | first2=Fred | last3=Taylor | first3=Richard | title=Modularity of certain potentially Barsotti–Tate Galois representations | doi=10.1090/S0894-0347-99-00287-8 | mr=1639612 | year=1999 | journal=[[Journal of the American Mathematical Society]] | issn=0894-0347 | volume=12 | issue=2 | pages=521–567| doi-access=free }}
*{{Citation | editor1-last=Cornell | editor1-first=Gary | editor2-last=Silverman | editor2-first=Joseph H. | editor2-link=Joseph H. Silverman | editor3-last=Stevens | editor3-first=Glenn | title=Modular forms and Fermat's last theorem | url=https://books.google.com/books?id=Va-quzVwtMsC | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-0-387-94609-2| mr=1638473 | year=1997}}
*{{Citation | last1=Darmon | first1=Henri | title=A proof of the full Shimura–Taniyama–Weil conjecture is announced | url=https://www.ams.org/notices/199911/comm-darmon.pdf | mr=1723249 | year=1999 | journal=[[Notices of the American Mathematical Society]] | issn=0002-9920 | volume=46 | issue=11 | pages=1397–1401}}Contains a gentle introduction to the theorem and an outline of the proof.
*{{Citation | last1=Diamond | first1=Fred | title=On deformation rings and Hecke rings | doi=10.2307/2118586 | mr=1405946 | year=1996 | journal=[[Annals of Mathematics]] |series=Second Series | issn=0003-486X | volume=144 | issue=1 | pages=137–166| jstor=2118586 }}
*{{Citation | last1=Freitas | first1=Nuno | last2 = Le Hung | first2 = Bao V. | last3 = Siksek | first3 = Samir | title=Elliptic curves over real quadratic fields are modular | year=2015 | journal=[[Inventiones Mathematicae]] | issn=0020-9910 | volume=201 | issue=1 | pages=159–206 | doi=10.1007/s00222-014-0550-z | mr=3359051| arxiv=1310.7088 | bibcode=2015InMat.201..159F | s2cid=119132800 }}
*{{Citation | last1=Frey | first1=Gerhard | title=Links between stable elliptic curves and certain Diophantine equations | mr=853387 | year=1986 | journal=Annales Universitatis Saraviensis. Series Mathematicae | issn=0933-8268 | volume=1 | issue=1 | pages=iv+40}}
*{{Citation | last1=Mazur | first1=Barry | author1-link=Barry Mazur | title=Number theory as gadfly | doi=10.2307/2324924 | mr=1121312 | year=1991 | journal=[[American Mathematical Monthly|The American Mathematical Monthly]] | issn=0002-9890 | volume=98 | issue=7 | pages=593–610| jstor=2324924 }} Discusses the Taniyama–Shimura–Weil conjecture 3 years before it was proven for infinitely many cases.
*{{Citation | last1=Ribet | first1=Kenneth A. | title=On modular representations of Gal({{overline|'''Q'''}}/'''Q''') arising from modular forms | doi=10.1007/BF01231195 | mr=1047143 | year=1990 | journal=[[Inventiones Mathematicae]] | issn=0020-9910 | volume=100 | issue=2 | pages=431–476| bibcode=1990InMat.100..431R | hdl=10338.dmlcz/147454 | s2cid=120614740 | hdl-access=free }}
*{{Citation | last1=Serre | first1=Jean-Pierre | author1-link=Jean-Pierre Serre | title=Sur les représentations modulaires de degré 2 de Gal({{overline|Q}}/Q) | doi=10.1215/S0012-7094-87-05413-5 | mr=885783 | year=1987 | journal=[[Duke Mathematical Journal]] | issn=0012-7094 | volume=54 | issue=1 | pages=179–230}}
*{{Citation | last1=Shimura | first1=Goro | title=Yutaka Taniyama and his time. Very personal recollections | doi=10.1112/blms/21.2.186 | mr=976064 | year=1989 | journal=The Bulletin of the London Mathematical Society | issn=0024-6093 | volume=21 | issue=2 | pages=186–196| doi-access=free }}
*{{Citation | last1=Singh | first1=Simon | author-link=Simon Singh | title = Fermat's Last Theorem | year=1997| publisher=Fourth Estate | isbn=978-1-85702-521-7}}
*{{citation|last=Taniyama|first=Yutaka |journal=Sugaku|volume=7|page=269|year=1956|title=Problem 12|language=ja}} English translation in {{harv|Shimura|1989|loc=p. 194}}
*{{Citation | last1=Taylor | first1=Richard | last2=Wiles | first2=Andrew | author2-link=Andrew Wiles | title=Ring-theoretic properties of certain Hecke algebras | doi=10.2307/2118560 | mr=1333036 | year=1995 | journal=[[Annals of Mathematics]] |series=Second Series | issn=0003-486X | volume=141 | issue=3 | pages=553–572| jstor=2118560 | citeseerx=10.1.1.128.531 }}
*{{Citation | last1=Weil | first1=André | author1-link=André Weil | title=Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen | doi=10.1007/BF01361551 | mr=0207658 | year=1967 | journal=[[Mathematische Annalen]] | issn=0025-5831 | volume=168 | pages=149–156| s2cid=120553723 }}
*{{Citation | last1=Wiles | first1=Andrew | author1-link=Andrew Wiles | title=Modular elliptic curves and Fermat's last theorem | jstor=2118559 | mr=1333035 | year=1995a | journal=[[Annals of Mathematics]] |series=Second Series | issn=0003-486X | volume=141 | issue=3 | pages=443–551 | doi=10.2307/2118559| citeseerx=10.1.1.169.9076 }}
*{{Citation | last1=Wiles | first1=Andrew | author1-link=Andrew Wiles | title=Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994) | publisher=Birkhäuser | location=Basel, Boston, Berlin | mr=1403925 | year=1995b | chapter=Modular forms, elliptic curves, and Fermat's last theorem | pages=243–245}}
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