Kontsevich's conjecture
Category theoretic mirror symmetry conjecture
When there exists mirror relation between X1 and X2, derived category of X1's coherent sheaf and derived Fukaya category defined from X2's symplectic structure become equivalence.
M. Kontsevich. Homological algebra of mirror symmetry, Vol. 1 of Proceedings of ICM. 1995.
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[Note by TANAKA Akio]
In the near future, symplectic geometry may be written by derived category. If so, complexed image of symplectic geometry's some theorems will become clearer.
References
Category theoretic mirror symmetry conjecture
When there exists mirror relation between X1 and X2, derived category of X1's coherent sheaf and derived Fukaya category defined from X2's symplectic structure become equivalence.
M. Kontsevich. Homological algebra of mirror symmetry, Vol. 1 of Proceedings of ICM. 1995.
-----------------------------------------------------------------------------------------------------------------------
[Note by TANAKA Akio]
In the near future, symplectic geometry may be written by derived category. If so, complexed image of symplectic geometry's some theorems will become clearer.
References
- Mirror Symmetry Conjecture on Rational Curve / Symplectic Language Theory
- Homological Mirror Symmetry Conjecture by KONTSEVICH / Symplectic Language Theory
- Quantization of Language / Floer Homology Language
Read more: http://srfl-theory.webnode.com/news/kontsevichs-conjecture-category-theoretic-mirror-symmetry-conjecture/
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