About: Drinfeld upper half plane

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In mathematics, the Drinfeld upper half plane is a rigid analytic space analogous to the usual upper half plane for function fields, introduced by Drinfeld. It is defined to be P1(C)\P1(F∞), where F is a function field of a curve over a finite field, F∞ its completion at ∞, and C the completion of the algebraic closure of F∞.

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  • In mathematics, the Drinfeld upper half plane is a rigid analytic space analogous to the usual upper half plane for function fields, introduced by Drinfeld. It is defined to be P1(C)\P1(F∞), where F is a function field of a curve over a finite field, F∞ its completion at ∞, and C the completion of the algebraic closure of F∞. The analogy with the usual upper half plane arises from the fact that the global function field F is analogous to the rational numbers Q. Then, F∞ is the real numbers R and the algebraic closure of F∞ is the complex numbers C (which are already complete). Finally, P1(C) is the Riemann sphere, so P1(C)\P1(R) is the upper half plane together with the lower half plane. (en)
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  • In mathematics, the Drinfeld upper half plane is a rigid analytic space analogous to the usual upper half plane for function fields, introduced by Drinfeld. It is defined to be P1(C)\P1(F∞), where F is a function field of a curve over a finite field, F∞ its completion at ∞, and C the completion of the algebraic closure of F∞. (en)
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  • Drinfeld upper half plane (en)
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