About: Lafforgue's theorem

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In mathematics, Lafforgue's theorem, due to Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields, by giving a correspondence between automorphic forms on these groups and representations of Galois groups. The Langlands conjectures were introduced by Langlands and describe a correspondence between representations of the Weil group of an algebraic function field and representations of algebraic groups over the function field, generalizing class field theory of function fields from abelian Galois groups to non-abelian Galois groups.

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rdfs:label	Lafforgue's theorem (en) ラフォルグの定理 (ja)
rdfs:comment	In mathematics, Lafforgue's theorem, due to Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields, by giving a correspondence between automorphic forms on these groups and representations of Galois groups. The Langlands conjectures were introduced by Langlands and describe a correspondence between representations of the Weil group of an algebraic function field and representations of algebraic groups over the function field, generalizing class field theory of function fields from abelian Galois groups to non-abelian Galois groups. (en) 数学のラフォルグの定理（ラフォルグの定理、英: Lafforgue's theorem）とは、代数関数体の一般線型群上の保型形式とガロア群の表現とを対応付けるローラン・ラフォルグによって証明された定理であり、この場合におけるラングランズ・プログラムを確立するものである。ラングランズ予想は、ラングランズによって提唱された代数関数体のヴェイユ群の表現とその関数体上の代数群の表現の間の対応を予想するもので、関数体の類体論をアーベルなガロア群から非アーベルなガロア群へ一般化するものである。 (ja)
dcterms:subject	Conjectures Representation theory of Lie groups Class field theory Theorems in algebraic number theory Automorphic forms Langlands program Theorems in representation theory
Wikipage page ID	32295019 (xsd:integer)
Wikipage revision ID	1020395848 (xsd:integer)
Link from a Wikipage to another Wikipage	Algebraic function field Algebraic group Level structure (algebraic geometry) Conjectures Representation theory of Lie groups Mathematics General linear group Publications Mathématiques de l'IHÉS Galois group Langlands program Local Langlands conjectures American Mathematical Society Class field theory Theorems in algebraic number theory Laurent Lafforgue Automorphic forms Automorphic form Langlands program Theorems in representation theory Class field theory Ramanujan–Petersson conjecture Weil group Springer-Verlag Artin map ℓ-adic cohomology Shtuka
Link from a Wikipage to an external page	https://www.ams.org/publications/online-books/pspum332-index https://books.google.com/books%3Fid=_p5qAAAAMAAJ http://publications.ias.edu/rpl/section/21 http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/JL.html%23book https://arxiv.org/abs/math.AG/0003131 https://arxiv.org/abs/math.NT/0212399 https://arxiv.org/abs/math.NT/0212417 http://publications.ias.edu/rpl/ https://www.ihes.fr/~lafforgue/publications.html http://www.numdam.org/item%3Fid=PMIHES_1980__52__137_0 http://www.math.uni-bielefeld.de/documenta/xvol-icm/07/Lafforgue.MAN.html http://www.math.uni-bonn.de/ag/alggeom/preprints/lafforgue.pdf
sameAs	Lafforgue's theorem Lafforgue's theorem Lafforgue's theorem Lafforgue's theorem Lafforgue's theorem
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has abstract	In mathematics, Lafforgue's theorem, due to Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields, by giving a correspondence between automorphic forms on these groups and representations of Galois groups. The Langlands conjectures were introduced by Langlands and describe a correspondence between representations of the Weil group of an algebraic function field and representations of algebraic groups over the function field, generalizing class field theory of function fields from abelian Galois groups to non-abelian Galois groups. (en) 数学のラフォルグの定理（ラフォルグの定理、英: Lafforgue's theorem）とは、代数関数体の一般線型群上の保型形式とガロア群の表現とを対応付けるローラン・ラフォルグによって証明された定理であり、この場合におけるラングランズ・プログラムを確立するものである。ラングランズ予想は、ラングランズによって提唱された代数関数体のヴェイユ群の表現とその関数体上の代数群の表現の間の対応を予想するもので、関数体の類体論をアーベルなガロア群から非アーベルなガロア群へ一般化するものである。 (ja)
prov:wasDerivedFrom	wikipedia-en:Lafforgue's_theorem?oldid=1020395848&ns=0
page length (characters) of wiki page	7002 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Lafforgue's_theorem
is Link from a Wikipage to another Wikipage of	List of long mathematical proofs Langlands program Laurent Lafforgue Ramanujan–Petersson conjecture List of theorems List of unsolved problems in mathematics
is known for of	Laurent Lafforgue
is known for of	Laurent Lafforgue
is foaf:primaryTopic of	wikipedia-en:Lafforgue's_theorem

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