Fundamental Domains of Some Drinfeld Modular Curves
نویسندگان
چکیده
We construct fundamental domains for arithmetic subgroups of Γ = GL2(Fq [t]). Given ∆ ⊇ Γ(a) we construct a contracted form T of the Bruhat-Tits tree T and a fundamental domain F of ∆ acting on T. We define a lift of F to F ⊂ T called the “bipartite” lift. We show that F is a fundamental domain of ∆ acting on T precisely when F is “∆-compressed.”
منابع مشابه
On the Number of Rational Points on Drinfeld Modular Varieties over Finite Fields
Drinfeld and Vladut proved that Drinfeld modular curves have many Fq2 -rational points compared to their genera. We propose a conjectural generalization of this result to higher dimensional Drinfeld modular varieties, and prove a theorem giving some evidence for the conjecture.
متن کاملIntroduction to Drinfeld Modules
(1) Explicit class field theory for global function fields (just as torsion of Gm gives abelian extensions of Q, and torsion of CM elliptic curves gives abelian extension of imaginary quadratic fields). Here global function field means Fp(T ) or a finite extension. (2) Langlands conjectures for GLn over function fields (Drinfeld modular varieties play the role of Shimura varieties). (3) Modular...
متن کاملExplicit towers of Drinfeld modular curves
We give explicit equations for the simplest towers of Drinfeld modular curves over any finite field, and observe that they coincide with the asymptotically optimal towers of curves constructed by Garcia and Stichtenoth.
متن کاملThe André-Oort conjecture for products of Drinfeld modular curves
Let Z = X1×· · ·×Xn be a product of Drinfeld modular curves. We characterize those algebraic subvarieties X ⊂ Z containing a Zariski-dense set of CM points, i.e. points corresponding to n-tuples of Drinfeld modules with complex multiplication (and suitable level structure). This is a characteristic p analogue of a special case of the André-Oort conjecture.
متن کاملThe Rigid Analytical Regulator and K2 of Drinfeld Modular Curves
We evaluate a rigid analytical analogue of the Beilinson-Bloch-Deligne regulator on certain explicit elements in the K2 of Drinfeld modular curves, constructed from analogues of modular units, and relate its value to special values of L-series using the Rankin-Selberg method.
متن کامل