TY - JOUR
T1 - Categorical mirror symmetry
T2 - The elliptic curve
AU - Polishchuk, Alexander
AU - Zaslow, Eric
PY - 1998/3
Y1 - 1998/3
N2 - We describe an 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.
AB - We describe an 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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U2 - 10.4310/ATMP.1998.v2.n2.a9
DO - 10.4310/ATMP.1998.v2.n2.a9
M3 - Article
AN - SCOPUS:0001623086
VL - 2
SP - 443
EP - 470
JO - Advances in Theoretical and Mathematical Physics
JF - Advances in Theoretical and Mathematical Physics
SN - 1095-0761
IS - 2
ER -