2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/198925We describe an isomorphism of categories conjectured by Kontsevich. If $M$ and $\widetilde{M}$ 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 $\widetilde{M}.$ We prove this equivalence when $M$ is an elliptic curve and $\widetilde{M}$ is its dual curve, exhibiting the dictionary in detail.harvmac, 29 pages (big); updated with correctionsAlgebraic GeometryHigh Energy Physics - Theorytext