| This thesis explores the relation between three quasi-equivalent categories: the category of coherent sheaves on a toric variety, the category of certain constructible sheaves on a real vector space, and a certain Fukaya category of the cotangent bundle of that real vector space. The quasi-equivalence between the Fukaya category and the category of coherent sheaves is achieved by a T-duality process and is regarded as a version of homological mirror symmetry, while the quasi-equivalence between the category of certain constructible sheaves and the category of coherent sheaves is a new relation called coherent-constructible correspondence, which categorifies Morelli's theorem at the level of K-theory [Mo]. |
