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For p≥3 an odd prime and a nonnegative integer r≤p−2, we prove a conjecture of Breuil on lattices in semi-stable representations, that is, the anti-equivalence of categories between the category of strongly divisible lattices of weight r and the category of Galois stable 
-lattices in semi-stable p-adic Galois representations with Hodge–Tate weights in {0,…,r}.
