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In algebraic geometry, the Kempf vanishing theorem, introduced by Kempf, states that the higher cohomology group Hi(G/B,L(λ)) (i > 0) vanishes whenever λ is a dominant weight of B. Here G is a reductive algebraic group over an algebraically closed field, B a Borel subgroup, and L(λ) a line bundle associated to λ. In characteristic 0 this is a special case of the Borel–Weil–Bott theorem, but unlike the Borel–Weil–Bott theorem, the Kempf vanishing theorem still holds in positive characteristic. and found simpler proofs of the Kempf vanishing theorem using the Frobenius morphism.

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  • Kempf vanishing theorem (en)
  • Kempfs försvinnandesats (sv)
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  • In algebraic geometry, the Kempf vanishing theorem, introduced by Kempf, states that the higher cohomology group Hi(G/B,L(λ)) (i > 0) vanishes whenever λ is a dominant weight of B. Here G is a reductive algebraic group over an algebraically closed field, B a Borel subgroup, and L(λ) a line bundle associated to λ. In characteristic 0 this is a special case of the Borel–Weil–Bott theorem, but unlike the Borel–Weil–Bott theorem, the Kempf vanishing theorem still holds in positive characteristic. and found simpler proofs of the Kempf vanishing theorem using the Frobenius morphism. (en)
  • Inom algebraisk geometri är Kempfs frösvinnandesats, introducerad av, ett resultat som säger att de högre kohomologigrupperna Hi(G/B,L(λ)) (i > 0) försvinner om λ är en dominerande vikt av B. Här är G en över en , B en Boreldelgrupp och L(λ) en linjeknippe associerad till λ. I karakteristik 0 är detta ett specialfall av , men till skillnad från Borel–Weil–Botts sats gäller Kempfs försvinnandesats även i positiv karakteristik. ) och ) upptäckte enklare bevis av satsen genom att använda Frobeniusmorfin. (sv)
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  • In algebraic geometry, the Kempf vanishing theorem, introduced by Kempf, states that the higher cohomology group Hi(G/B,L(λ)) (i > 0) vanishes whenever λ is a dominant weight of B. Here G is a reductive algebraic group over an algebraically closed field, B a Borel subgroup, and L(λ) a line bundle associated to λ. In characteristic 0 this is a special case of the Borel–Weil–Bott theorem, but unlike the Borel–Weil–Bott theorem, the Kempf vanishing theorem still holds in positive characteristic. and found simpler proofs of the Kempf vanishing theorem using the Frobenius morphism. (en)
  • Inom algebraisk geometri är Kempfs frösvinnandesats, introducerad av, ett resultat som säger att de högre kohomologigrupperna Hi(G/B,L(λ)) (i > 0) försvinner om λ är en dominerande vikt av B. Här är G en över en , B en Boreldelgrupp och L(λ) en linjeknippe associerad till λ. I karakteristik 0 är detta ett specialfall av , men till skillnad från Borel–Weil–Botts sats gäller Kempfs försvinnandesats även i positiv karakteristik. ) och ) upptäckte enklare bevis av satsen genom att använda Frobeniusmorfin. (sv)
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