On a Teichmüller functor between the categories of complex and noncommutative tori
نویسنده
چکیده
A covariant functor from category of complex tori to the category of noncommutative tori is constructed. The functor maps isomorphic complex tori to the Morita equivalent noncommutative tori. Our construction is based on the Teichmüller theory of Riemann surfaces.
منابع مشابه
On a Teichmüller functor between the categories of complex tori and the Effros–Shen algebras
A covariant functor from the category of the complex tori to the category of the Effros–Shen algebras is constructed. The functor maps isomorphic complex tori to the stably isomorphic Effros–Shen algebras. Our construction is based on the Teichmüller theory of the
متن کاملOn a desingularization of the moduli space of noncommutative tori
It is shown that the moduli space of the noncommutative tori Aθ admits a natural desingularization by the group Ext (Aθ, Aθ). Namely, we prove that the moduli space of pairs (Aθ, Ext (Aθ, Aθ)) is homeomorphic to a punctured two-dimensional sphere. The proof is based on a correspondence (a covariant functor) between the complex and noncommutative tori.
متن کاملCategories of holomorphic line bundles on higher dimensional noncommutative complex tori
We construct explicitly noncommutative deformations of categories of holomorphic line bundles over higher dimensional tori. Our basic tools are Heisenberg modules over noncommutative tori and complex/holomorphic structures on them introduced by A. Schwarz. We obtain differential graded (DG) categories as full subcategories of curved DG categories of Heisenberg modules over the complex noncommut...
متن کاملRemark on the rank of elliptic curves
A covariant functor on the elliptic curves with complex multiplication is constructed. The functor takes values in the noncommutative tori with real multiplication. A conjecture on the rank of an elliptic curve is formulated.
متن کاملDuality and Equivalence of Module Categories in Noncommutative Geometry Ii: Mukai Duality for Holomorphic Noncommutative Tori
This is the second in a series of papers intended to set up a framework to study categories of modules in the context of non-commutative geometries. In [3] we introduced the basic DG category PA• , the perfect category of A•, which corresponded to the category of coherent sheaves on a complex manifold. In this paper we enlarge this category to include objects which correspond to quasi-coherent ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009