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- Adele_ring abstract "In algebraic number theory and topological algebra, the adele ring (other names are the adelic ring, the ring of adeles) is a self-dual topological ring built on the field of rational numbers (or, more generally, any algebraic number field). It involves in a symmetric way all the completions of the field.The adele ring was introduced by Claude Chevalley for the purposes of simplifying and clarifying class field theory. It has also found applications outside that area.The adele ring and its relation to the number field are among the most fundamental objects in number theory. The quotient of its multiplicative group by the multiplicative group of the algebraic number field is the central object in class field theory. It is a central principle of Diophantine geometry to study solutions of polynomials equations in number fields by looking at their solutions in the larger complete adele ring, where it is generally easier to detect solutions, and then deciding which of them come from the number field.The word "adele" is short for "additive idele" and it was invented by André Weil. The previous name was the valuation vectors. The ring of adeles was historically preceded by the ring of repartitions, a construction which avoids completions, and is today sometimes referred to as pre-adele.".
- Adele_ring wikiPageID "247978".
- Adele_ring wikiPageLength "9957".
- Adele_ring wikiPageOutDegree "57".
- Adele_ring wikiPageRevisionID "671915801".
- Adele_ring wikiPageWikiLink Abelian_varieties.
- Adele_ring wikiPageWikiLink Abelian_variety.
- Adele_ring wikiPageWikiLink Academic_Press.
- Adele_ring wikiPageWikiLink Adelic_algebraic_group.
- Adele_ring wikiPageWikiLink Algebraic_group.
- Adele_ring wikiPageWikiLink Algebraic_number_field.
- Adele_ring wikiPageWikiLink Algebraic_number_theory.
- Adele_ring wikiPageWikiLink André_Weil.
- Adele_ring wikiPageWikiLink Artin_reciprocity_law.
- Adele_ring wikiPageWikiLink Birch_and_Swinnerton-Dyer_conjecture.
- Adele_ring wikiPageWikiLink Category:Algebraic_number_theory.
- Adele_ring wikiPageWikiLink Category:Topological_algebra.
- Adele_ring wikiPageWikiLink Chinese_remainder_theorem.
- Adele_ring wikiPageWikiLink Class_field_theory.
- Adele_ring wikiPageWikiLink Claude_Chevalley.
- Adele_ring wikiPageWikiLink Co-compact.
- Adele_ring wikiPageWikiLink Diophantine_geometry.
- Adele_ring wikiPageWikiLink Discrete_group.
- Adele_ring wikiPageWikiLink Field_(mathematics).
- Adele_ring wikiPageWikiLink Function_field_of_an_algebraic_variety.
- Adele_ring wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Adele_ring wikiPageWikiLink Group_(mathematics).
- Adele_ring wikiPageWikiLink Harmonic_analysis.
- Adele_ring wikiPageWikiLink Idele.
- Adele_ring wikiPageWikiLink Idele_group.
- Adele_ring wikiPageWikiLink Inverse_limit.
- Adele_ring wikiPageWikiLink John_Tate.
- Adele_ring wikiPageWikiLink Kazuya_Kato.
- Adele_ring wikiPageWikiLink Kenkichi_Iwasawa.
- Adele_ring wikiPageWikiLink Langlands_correspondence.
- Adele_ring wikiPageWikiLink Langlands_program.
- Adele_ring wikiPageWikiLink Local_class_field_theory.
- Adele_ring wikiPageWikiLink Locally_compact.
- Adele_ring wikiPageWikiLink Locally_compact_space.
- Adele_ring wikiPageWikiLink P-adic_integer.
- Adele_ring wikiPageWikiLink P-adic_integers.
- Adele_ring wikiPageWikiLink P-adic_number.
- Adele_ring wikiPageWikiLink Pontryagin_duality.
- Adele_ring wikiPageWikiLink Profinite_group.
- Adele_ring wikiPageWikiLink Quadratic_form.
- Adele_ring wikiPageWikiLink Rational_number.
- Adele_ring wikiPageWikiLink Real_number.
- Adele_ring wikiPageWikiLink Restricted_product.
- Adele_ring wikiPageWikiLink Riemann–Roch_theorem.
- Adele_ring wikiPageWikiLink Robert_Kottwitz.
- Adele_ring wikiPageWikiLink Schwartz–Bruhat_function.
- Adele_ring wikiPageWikiLink Simply_connected.
- Adele_ring wikiPageWikiLink Simply_connected_space.
- Adele_ring wikiPageWikiLink Spencer_Bloch.
- Adele_ring wikiPageWikiLink Springer-Verlag.
- Adele_ring wikiPageWikiLink Springer_Science+Business_Media.
- Adele_ring wikiPageWikiLink Tamagawa_number.
- Adele_ring wikiPageWikiLink Tates_thesis.
- Adele_ring wikiPageWikiLink Tensor_product_of_algebras.
- Adele_ring wikiPageWikiLink Topological_algebra.
- Adele_ring wikiPageWikiLink Topological_ring.
- Adele_ring wikiPageWikiLink V._I._Chernousov.
- Adele_ring wikiPageWikiLink Weil_conjecture_on_Tamagawa_numbers.
- Adele_ring wikiPageWikiLinkText "Adele ring".
- Adele_ring wikiPageWikiLinkText "Adele ring#Idele group".
- Adele_ring wikiPageWikiLinkText "Adele".
- Adele_ring wikiPageWikiLinkText "Adele_ring#Idèle group".
- Adele_ring wikiPageWikiLinkText "adele ring".
- Adele_ring wikiPageWikiLinkText "adele".
- Adele_ring wikiPageWikiLinkText "adeles".
- Adele_ring wikiPageWikiLinkText "adelic".
- Adele_ring wikiPageWikiLinkText "ring of adeles".
- Adele_ring hasPhotoCollection Adele_ring.
- Adele_ring wikiPageUsesTemplate Template:Citation.
- Adele_ring wikiPageUsesTemplate Template:Neukirch_ANT.
- Adele_ring subject Category:Algebraic_number_theory.
- Adele_ring subject Category:Topological_algebra.
- Adele_ring hypernym Ring.
- Adele_ring type AnatomicalStructure.
- Adele_ring comment "In algebraic number theory and topological algebra, the adele ring (other names are the adelic ring, the ring of adeles) is a self-dual topological ring built on the field of rational numbers (or, more generally, any algebraic number field). It involves in a symmetric way all the completions of the field.The adele ring was introduced by Claude Chevalley for the purposes of simplifying and clarifying class field theory.".
- Adele_ring label "Adele ring".
- Adele_ring sameAs Anell_adèlic.
- Adele_ring sameAs Adelring.
- Adele_ring sameAs Adelen_rengas.
- Adele_ring sameAs Anneau_adélique.
- Adele_ring sameAs アデール環.
- Adele_ring sameAs 아델_환.
- Adele_ring sameAs Adele-ring.
- Adele_ring sameAs Anel_adélico.
- Adele_ring sameAs m.01kvx7.
- Adele_ring sameAs Q355356.
- Adele_ring sameAs Q355356.
- Adele_ring sameAs 賦值向量環.
- Adele_ring wasDerivedFrom Adele_ring?oldid=671915801.
- Adele_ring isPrimaryTopicOf Adele_ring.