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We describe jm isomorphism of categories conjectured by Kontsevich. If M and M are mirror pairs then the conjectural equivalence is between the derived category of coherent sheaves on M and a suitable version of Fukaya's category of Lagrangian submanifolds^on M. We prove this equivalence when M is an elliptic curve and M is its dual curve, exhibiting the dictionary in detail.

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We show that elliptic solutions of classical Yang-Baxter equation (CYBE) can be obtained from triple Massey products on an elliptic curve. We introduce the associative version of this equation which has two spectral parameters and construct its elliptic solutions. We also study some degenerations of these solutions.

1.1.1. Results on sheaves of t-structures. In section 2 we are given a nondegenerate t-structure (D(X) ≤0 , D(X) ≥0 ) with heart C = D(X) ≤0 ∩ D(X) ≥0 (see section 1.2 for definitions and a brief introduction). For a smooth projective variety S with ample line bundle L we defineAssuming that C is noetherian we prove