Talk:Decomposition theorem of Beilinson, Bernstein and Deligne

How does the hard Lefschetz theorem induce the decomposition?
The article states: This hard Lefschetz isomorphism induces canonical isomorphisms
 * $$Rf_* (\mathbb Q) \stackrel \cong \to \bigoplus_{i=-d}^{d} R^{d+i} f_*(\mathbb Q)[-d-i].$$

But I how does this follow? Does anyone know a reference?

Nielius (talk) 08:50, 8 March 2017 (UTC)


 * added a reference.Jakob.scholbach (talk) 20:40, 8 March 2017 (UTC)

Suggestions

 * 1) There needs to be better examples showing what the decomposition theorem actually does. For example, showing the decomposition theorem for blow-ups, resolutions of singularities, and springer resolutions.
 * 2) Computation of intersection cohomology of singular varieties
 * 3) Statement and examples of perverse spectral sequence
 * 4) The decomposition theorem should be stated for intersection cohomology sheaves. This is a much better description because it shows us how the simple objects decompose.


 * I agree with all your suggestions. Please go ahead, this is the encyclopaedia that everyone can edit! Jakob.scholbach (talk) 12:37, 10 June 2017 (UTC)