منابع مشابه
The Riemann-roch Theorem and Serre Duality
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Let H be an involutory Hopf algebra over a field of characteristic zero, M and N two finite dimensional left H-modules such that M ⊗ N is a semisimple H-module. Then M and N are semisimple H-modules. This is a generalization of a theorem proved by J.-P. Serre for group algebras. A version of the theorem above for monoidal categories is also given.
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In this note we prove the Serre duality theorem for the cohomology of coherent sheaves on a projective scheme. First we do the case of projective space itself. Then on an arbitrary projective scheme X, we show that there is a coherent sheaf ω◦ X , which plays the role in duality theory similar to the canonical sheaf of a nonsingular variety. In particular, if X is Cohen-Macaulay, it gives a dua...
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We generalize the classical theorem of Serre on the non-triviality of infinitely many homotopy groups of 1-connected finite CW-complexes to CW-complexes where the cohomology groups either grow too fast or do not grow faster than a certain rate given by connectivity. For example, this result can be applied to iterated suspensions of finite Postnikov systems and certain spaces with finitely gener...
متن کاملThe adjunction problem and a theorem of Serre
In this note we prove injectivity and relative asphericity for “layered” systems of equations over torsion-free groups, when the exponent matrix is invertible over Z. We also give elementary geometric proofs of results due to Bogley–Pride and Serre that are used in the proof of the main theorem. AMS Classification 20E22, 20F05; 57M20, 57Q05
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-05101-1