Finiteness results for modular curves of genus at least 2
نویسندگان
چکیده
منابع مشابه
Finiteness Results for Modular Curves of Genus at Least 2
A curve X over Q is modular if it is dominated by X1(N) for some N ; if in addition the image of its jacobian in J1(N) is contained in the new subvariety of J1(N), then X is called a new modular curve. We prove that for each g ≥ 2, the set of new modular curves over Q of genus g is finite and computable. For the computability result, we prove an algorithmic version of the de Franchis-Severi The...
متن کاملFiniteness Results for Modular Curves of Genus at Least
A curve X over Q is modular if it is dominated by X1(N) for some N; if in addition the image of its jacobian in J1(N) is contained in the new subvariety of J1(N), then X is called a new modular curve. We prove that for each g ≥ 2, the set of new modular curves over Q of genus g is finite and computable. For the computability result, we prove an algorithmic version of the de Franchis-Severi Theo...
متن کاملModular curves of genus 2
We prove that there are exactly 149 genus two curves C defined over Q such that there exists a nonconstant morphism π : X1(N)→ C defined over Q and the jacobian of C is Q-isogenous to the abelian variety Af attached by Shimura to a newform f ∈ S2(Γ1(N)). We determine the corresponding newforms and present equations for all these curves.
متن کاملComputational Aspects of Curves of Genus at Least 2
This survey discusses algorithms and explicit calculations for curves of genus at least 2 and their Jacobians, mainly over number fields and finite fields. Miscellaneous examples and a list of possible future projects are given at the end.
متن کاملFiniteness Results for Teichmüller Curves
We show that for each genus there are only finitely many algebraically primitive Teichmüller curves C, such that i) C lies in the hyperelliptic locus and ii) C is generated by an abelian differential with two zeros of order g − 1. We prove moreover that for these Teichmüller curves the trace field of the affine group is not only totally real but cyclotomic.
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2005
ISSN: 1080-6377
DOI: 10.1353/ajm.2005.0037