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- Weil–Châtelet_group abstract "In arithmetic geometry, the Weil–Châtelet group or WC-group of an algebraic group such as an abelian variety A defined over a field K is the abelian group of principal homogeneous spaces for A, defined over K. Tate (1958) named it for François Châtelet (1946) who introduced it for elliptic curves, and Weil (1955), who introduced it for more general groups. It plays a basic role in the arithmetic of abelian varieties, in particular for elliptic curves, because of its connection with infinite descent.It can be defined directly from Galois cohomology, as H1(GK,A), where GK is the absolute Galois group of K. It is of particular interest for local fields and global fields, such as algebraic number fields. For K a finite field, Schmidt (1931) proved that the Weil–Châtelet group is trivial for elliptic curves, and Lang (1956) proved that it is trivial for any algebraic group.".
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- Weil–Châtelet_group wikiPageWikiLink Abelian_group.
- Weil–Châtelet_group wikiPageWikiLink Abelian_variety.
- Weil–Châtelet_group wikiPageWikiLink Absolute_Galois_group.
- Weil–Châtelet_group wikiPageWikiLink Algebraic_group.
- Weil–Châtelet_group wikiPageWikiLink Algebraic_number_field.
- Weil–Châtelet_group wikiPageWikiLink American_Journal_of_Mathematics.
- Weil–Châtelet_group wikiPageWikiLink American_Mathematical_Society.
- Weil–Châtelet_group wikiPageWikiLink Arithmetic_of_abelian_varieties.
- Weil–Châtelet_group wikiPageWikiLink Cambridge_University_Press.
- Weil–Châtelet_group wikiPageWikiLink Category:Number_theory.
- Weil–Châtelet_group wikiPageWikiLink Elliptic_curve.
- Weil–Châtelet_group wikiPageWikiLink Ernst_Sejersted_Selmer.
- Weil–Châtelet_group wikiPageWikiLink Field_(mathematics).
- Weil–Châtelet_group wikiPageWikiLink Finite_field.
- Weil–Châtelet_group wikiPageWikiLink Galois_cohomology.
- Weil–Châtelet_group wikiPageWikiLink Global_field.
- Weil–Châtelet_group wikiPageWikiLink Glossary_of_arithmetic_and_Diophantine_geometry.
- Weil–Châtelet_group wikiPageWikiLink Isogeny.
- Weil–Châtelet_group wikiPageWikiLink Local_field.
- Weil–Châtelet_group wikiPageWikiLink Mathematische_Zeitschrift.
- Weil–Châtelet_group wikiPageWikiLink Principal_homogeneous_space.
- Weil–Châtelet_group wikiPageWikiLink Proof_by_infinite_descent.
- Weil–Châtelet_group wikiPageWikiLink Selmer_group.
- Weil–Châtelet_group wikiPageWikiLink Springer_Science+Business_Media.
- Weil–Châtelet_group wikiPageWikiLink Tate–Shafarevich_group.
- Weil–Châtelet_group wikiPageWikiLink Torsion_(algebra).
- Weil–Châtelet_group wikiPageWikiLinkText "Weil–Châtelet group".
- Weil–Châtelet_group authorlink "François Châtelet".
- Weil–Châtelet_group first "François".
- Weil–Châtelet_group id "p/w097590".
- Weil–Châtelet_group last "Châtelet".
- Weil–Châtelet_group title "Weil-Châtelet group".
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- Weil–Châtelet_group wikiPageUsesTemplate Template:Distinguish.
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- Weil–Châtelet_group year "1946".
- Weil–Châtelet_group subject Category:Number_theory.
- Weil–Châtelet_group hypernym Group.
- Weil–Châtelet_group type Band.
- Weil–Châtelet_group type Diacritic.
- Weil–Châtelet_group type Field.
- Weil–Châtelet_group type Redirect.
- Weil–Châtelet_group type Thing.
- Weil–Châtelet_group comment "In arithmetic geometry, the Weil–Châtelet group or WC-group of an algebraic group such as an abelian variety A defined over a field K is the abelian group of principal homogeneous spaces for A, defined over K. Tate (1958) named it for François Châtelet (1946) who introduced it for elliptic curves, and Weil (1955), who introduced it for more general groups.".
- Weil–Châtelet_group label "Weil–Châtelet group".
- Weil–Châtelet_group differentFrom Weil_group.
- Weil–Châtelet_group sameAs Q7980204.
- Weil–Châtelet_group sameAs m.069ys7.
- Weil–Châtelet_group sameAs Weil–Châteletgrupp.
- Weil–Châtelet_group sameAs Q7980204.
- Weil–Châtelet_group wasDerivedFrom Weil–Châtelet_group?oldid=634815920.
- Weil–Châtelet_group isPrimaryTopicOf Weil–Châtelet_group.