About: Chevalley's structure theorem

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In algebraic geometry, Chevalley's structure theorem states that a smooth connected algebraic group over a perfect field has a unique normal smooth connected affine algebraic subgroup such that the quotient is an abelian variety. It was proved by (though he had previously announced the result in 1953), Barsotti , and . Over non-perfect fields there is still a smallest normal connected linear subgroup such that the quotient is an abelian variety, but the linear subgroup need not be smooth. A consequence of Chevalley's theorem is that any algebraic group over a field is quasi-projective.

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rdf:type	grape yago:WikicatTheoremsInAlgebraicGeometry yago:Abstraction100002137 yago:Communication100033020 yago:Group100031264 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293 yago:WikicatAlgebraicGroups
rdfs:label	Chevalley's structure theorem (en) Chevalleys struktursats (sv)
rdfs:comment	Inom algebraisk geometri är Chevalleys struktursats ett resultat som säger att en sammanhängande över en har en unik normal affin algebraisk delgrupp så att kvoten är en abelsk varietet. Satsen bevisades av (även om han hade tillkännagivit resultatet redan 1953), ) och ). (sv) In algebraic geometry, Chevalley's structure theorem states that a smooth connected algebraic group over a perfect field has a unique normal smooth connected affine algebraic subgroup such that the quotient is an abelian variety. It was proved by (though he had previously announced the result in 1953), Barsotti , and . Over non-perfect fields there is still a smallest normal connected linear subgroup such that the quotient is an abelian variety, but the linear subgroup need not be smooth. A consequence of Chevalley's theorem is that any algebraic group over a field is quasi-projective. (en)
dcterms:subject	Algebraic groups Theorems in algebraic geometry
Wikipage page ID	37657294 (xsd:integer)
Wikipage revision ID	1044759170 (xsd:integer)
Link from a Wikipage to another Wikipage	American Journal of Mathematics Algebraic group Algebraic groups Generalized Jacobian Algebraic geometry Theorems in algebraic geometry Abelian variety Albanese variety Foundations of algebraic geometry Néron–Ogg–Shafarevich criterion Perfect field Neron model
Link from a Wikipage to an external page	http://math.stanford.edu/~conrad/papers/chev.pdf
sameAs	Chevalley's structure theorem Chevalley's structure theorem Chevalley's structure theorem Chevalley's structure theorem Chevalley's structure theorem
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harvtxt dbt:Short_description dbt:Harvs
has abstract	In algebraic geometry, Chevalley's structure theorem states that a smooth connected algebraic group over a perfect field has a unique normal smooth connected affine algebraic subgroup such that the quotient is an abelian variety. It was proved by (though he had previously announced the result in 1953), Barsotti , and . Chevalley's original proof, and the other early proofs by Barsotti and Rosenlicht, used the idea of mapping the algebraic group to its Albanese variety. The original proofs were based on Weil's book Foundations of algebraic geometry and are hard to follow for anyone unfamiliar with Weil's foundations, but later gave an exposition of Chevalley's proof in scheme-theoretic terminology. Over non-perfect fields there is still a smallest normal connected linear subgroup such that the quotient is an abelian variety, but the linear subgroup need not be smooth. A consequence of Chevalley's theorem is that any algebraic group over a field is quasi-projective. (en) Inom algebraisk geometri är Chevalleys struktursats ett resultat som säger att en sammanhängande över en har en unik normal affin algebraisk delgrupp så att kvoten är en abelsk varietet. Satsen bevisades av (även om han hade tillkännagivit resultatet redan 1953), ) och ). (sv)
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page length (characters) of wiki page	4060 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Chevalley's_structure_theorem
is Link from a Wikipage to another Wikipage of	Algebraic group Generalized Jacobian Chevalley theorem List of theorems Chevalley's theorem on algebraic groups
is Wikipage redirect of	Chevalley's theorem on algebraic groups
is foaf:primaryTopic of	wikipedia-en:Chevalley's_structure_theorem

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