Trace formula on the p-adic upper half-plane
نویسندگان
چکیده
منابع مشابه
The p-adic upper half plane
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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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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conjugation, c, 5anti-cyclotomic p-adic L-function, L (π), 6Atkin–Serre operator, Θord, 13 canonical pairing, ( ,)A, 23convergent modular form, M(m,K), 14admissible, 15of finite tame level, M[ (m,K), 14stable, M[ (m,K)♥, 14universal, 15 distribution algebraA-related, D(A,K), 25ω-related, D(ω,K), 25π-related, D(π), 4 global Lubin–Tate different...
متن کاملA trace formula for finite upper half planes
In this paper, we prove a trace formula for finite upper half planes Hq. A brief outline is as follows: Fix a subgroup Γ ⊂ GL(2, Fq). The adjacency operators Aa act on functions in L(Γ\Hq); thus, we may consider Aa = Aa|L2(Γ\Hq). We prove a trace formula which is an equality between a weighted sum of the traces of the operators Aa and a sum over the conjugacy classes of Γ. The trace formula all...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2004
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2004.03.008