Drinfeld upper half plane
In
). 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.
References
- Drinfeld, V. G. (1976), "Coverings of p-adic symmetric domains", Akademija Nauk SSSR. Funkcional'nyi Analiz i ego Priloženija, 10 (2): 29–40, MR 0422290
- Genestier, Alain (1996), "Espaces symétriques de Drinfeld", Astérisque (234): 124, MR 1393015
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