On Drinfeld's universal formal group over thep-adic upper half plane
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منابع مشابه
On Drinfeld's universal formal group over the p-adic upper half plane
In his important paper "Coverings of p-adic symmetric regions" [Dr], Drinfeld showed that the p-adic upper half plane and its higher dimensional analogues serve as moduli spaces for certain rigidified formal groups with quaternionic multiplications. Given a formal group of the proper type, together with rigidifying data, over, say, a ring R on which p is nilpotent, Drinfeld constructs an R-valu...
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The p-adic upper half plane X is a rigid analytic variety over a p-adic field K, on which the group GL2(K) acts, that Mumford introduced (as a formal scheme) as part of his efforts to generalize Tate’s p-adic uniformization of elliptic curves to curves of higher genus. The Cp–valued points of X are just P(Cp)−P(K), with GL2(K) acting by linear fractional transformations. Mumford showed that the...
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This space was first introduced by Mumford, where it plays a key role in the generalization to higher genus of Tate’s theory of p-adic uniformization of elliptic curves with semistable reduction. Slightly later, Drinfeld and Cerednik showed that appropriate quotients of this space by discrete arithmetic subgroups of PGL2(K) coming from quaternion algebras yield Shimura curves. Since that time, ...
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For the finite field IFq of q elements (q odd) and a quadratic nonresidue α ∈ IFq, we define the distance function δ ( u+ v √ α, x+ y √ α ) = (u− x)2 − α(v − y)2 vy on the upper half plane Hq = {x + y √ α | x ∈ IFq, y ∈ IFq} ⊆ IFq2 . For two sets E ,F ⊂ Hq with #E = E, #F = F and a non-trivial additive character ψ on IFq, we give the following estimate ∣∣∣∣∣ ∑ w∈E,z∈F ψ(δ(w, z)) ∣∣∣∣∣ ≤ min {√ ...
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In the first part of the paper we show that the Busemann 1-compactification of the Siegel upper half plane of rank n: SHn = Sp(n, R)/Kn is the compactification as a bounded domain. In the second part of the paper we study certain properties of discrete groups Γ of biholomorphisms of SHn. We show that the set of accumulation points of the orbit Γ(Z) on the Shilov boundary of SHn is independent o...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 1989
ISSN: 0025-5831,1432-1807
DOI: 10.1007/bf01443357