ALGORITHM OF GLOBAL UNIFORMIZATION OF ALGEBRAIC CORRESPONDENCE

The Uniformization of Certain Algebraic Hypergeometric Functions

The hypergeometric functions nFn−1 are higher transcendental functions, but for certain parameter values they become algebraic. This occurs, e.g., if the defining hypergeometric differential equation has irreducible but imprimitive monodromy. It is shown that many algebraic nFn−1’s of this type can be represented as combinations of certain explicitly algebraic functions of a single variable, i....

The Jacquet-Langlands correspondence via `-adic uniformization

Krichever Correspondence for Algebraic Surfaces

In 70’s there was discovered a construction how to attach to some algebraicgeometric data an infinite-dimensional subspace in the space k((z)) of the Laurent power series. The construction was successfully used in the theory of integrable systems, particularly, for the KP and KdV equations [10, 19]. There were also found some applications to the moduli of algebraic curves [2, 3]. Now it is know...

Krichever correspondence for algebraic varieties

In the work is constructed new acyclic resolutions of quasicoherent sheaves. These resolutions is connected with multidimensional local fields. Then the obtained resolutions is applied for a construction of generalization of the Krichever map to algebraic varieties of any dimension. This map gives in the canonical way two k -subspaces B ⊂ k((z1)) . . . ((zn)) and W ⊂ k((z1)) . . . ((zn)) ⊕r fro...

The equivariant fundamental group, uniformization of real algebraic curves, and global complex analytic coordinates on Teichmüller spaces

Let X be a real algebraic curve of genus at least 2. We construct a global system of complex analytic coordinates on the Teichmuller space T(X) of complex algebraic curves of the same genus as X. . It induces a global system of real analytic coordinates on the real Teichmuller space of X. The method of construction consists of uniformizing the real algebraic curve X by the double half-plane CBR...