The proofs can be found in [Ber90] and the next pointers are with respect to the numeration in this reference: (1) follows from Theorem 1.2.1, Corollary 2.2.8 and Theorem 3.2.1, (2) is Theorem 3.4.8, (3) is Corollary 3.4.5, (4) is Proposition 3.4.6, (5) is Theorem 3.4.1(i), while (6) follows from Theorem 3.4.1(i) and Proposition 2.1.15. ∎