| 1. | A powerful tool for doing this is provided by spectral sequences.
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| 2. | They are one of the most powerful aspects of spectral sequences.
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| 3. | Spectral sequence # The spectral sequence of a filtered complex ).
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| 4. | Spectral sequence # The spectral sequence of a filtered complex ).
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| 5. | In particular the Serre spectral sequence was constructed for just this purpose.
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| 6. | Another common spectral sequence is the spectral sequence of a double complex.
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| 7. | Another common spectral sequence is the spectral sequence of a double complex.
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| 8. | What remains is to find a relationship between these two spectral sequences.
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| 9. | If our spectral sequence converges, then we conclude that:
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| 10. | The degeneration of the spectral sequence can be shown using Hodge theory.
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