/prog/ /proof/

1. Let SICP equal 'The Structure and Interpretation of Computer Programs'

Don’t be impatient, >>5-san.

Proposition 1.4. If ρ_f,λ is associated to a p-divisible group (the ordinary case is allowed) then
 ⑴ pr_n (H_F¹(Q_p,T)) = H_F¹(Q_p,T/λⁿ) and similarly for T*,T*/λⁿ.
 ⑵ H_F¹(Q_p,V_λⁿ) is the orthogonal complement of H_F¹(Q_p,V*_λⁿ) under Tate local duality between H¹(Q_p,V*_λⁿ) and similarly for W_λⁿ and W*_λⁿ replacing V_λⁿ and V*_λⁿ.
More generally these results hold for any crystalline representation Ѵ′ in place of Ѵ and λ′ a uniformizer in K′ where K′ is any finite extension of Q_p with K′ ⊂ End_Gal(Q̄p/Qp)Ѵ′.

(The proof is trivial, and is left as an exercise for the reader.)