On the Cuspidal Divisor Class Group of a Drinfeld Modular Curve
نویسندگان
چکیده
The theory of theta functions for arithmetic groups that act on the Drinfeld upper half-plane is extended to allow degenerate parameters. This is used to investigate the cuspidal divisor class groups of Drinfeld modular curves. These groups are nite for congruence subgroups and may be described through the corresponding quotients of the Bruhat-Tits tree by . The description given is fairly explicit, notably in the most important special case of Hecke congruence subgroups over a polynomial ring. 1991 Mathematics Subject Classi cation: 11G09, 11G18, 11F11, 11F12
منابع مشابه
On the Torsion of the Mordell-Weil Group of the Jacobian of Drinfeld Modular Curves
Let Y0(p) be the Drinfeld modular curve parameterizing Drinfeld modules of rank two over Fq[T ] of general characteristic with Hecke level p-structure, where p ⊳ Fq[T ] is a prime ideal of degree d. Let J0(p) denote the Jacobian of the unique smooth irreducible projective curve containing Y0(p). Define N(p) = q−1 q−1 , if d is odd, and define N(p) = q −1 q2−1 , otherwise. We prove that the tors...
متن کاملSTRUCTURE OF THE CUSPIDAL RATIONAL TORSION SUBGROUP OF J1(p n)
Let Γ be a congruence subgroup of SL(2,Z). The modular curve X(Γ) and its Jacobian variety J(Γ) are very important objects in number theory. For instance, the problem of determining all possible structures of (Q-)rational torsion subgroup of elliptic curves over Q is equivalent to that of determining whether the modular curves X1(N) have non-cuspidal rational points. Also, the celebrated theore...
متن کاملClass invariants and cyclotomic unit groups from special values of modular units . par Amanda
In this article we obtain class invariants and cyclotomic unit groups by considering specializations of modular units. We construct these modular units from functional solutions to higher order q-recurrence equations given by Selberg in his work generalizing the Rogers-Ramanujan identities. As a corollary, we provide a new proof of a result of Zagier and Gupta, originally considered by Gauss, r...
متن کاملClass invariants and cyclotomic unit groups from special values of modular units
In this article we obtain class invariants and cyclotomic unit groups by considering specializations of modular units. We construct these modular units from functional solutions to higher order q-recurrence equations given by Selberg in his work generalizing the Rogers-Ramanujan identities. As a corollary, we provide a new proof of a result of Zagier and Gupta, originally considered by Gauss, r...
متن کاملRational Torsion on the Generalized Jacobian of a Modular Curve With Cuspidal Modulus
We consider the generalized Jacobian J̃0(N) of a modular curveX0(N)with respect to a reduced divisor given by the sum of all cusps on it. WhenN is a power of a prime≥ 5, we exhibit that the group of rational torsion points J̃0(N)(Q)Tor tends to be much smaller than the classical Jacobian. 2010 Mathematics Subject Classification: Primary 14H40; Secondary 11G16, 11F03, 14G35.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014