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