Chevalley's structure theorem
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 Chevalley (though he had previously announced the result in 1953), , 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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Chevalley's structure theorem
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 Chevalley (though he had previously announced the result in 1953), , 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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In algebraic geometry, Chevall ...... r a field is quasi-projective.
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Inom algebraisk geometri är Ch ...... sultatet redan 1953), ) och ).
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In algebraic geometry, Chevall ...... r a field is quasi-projective.
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Inom algebraisk geometri är Ch ...... sultatet redan 1953), ) och ).
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Chevalley's structure theorem
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Chevalleys struktursats
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