Coregular spaces and genus one curves
نویسندگان
چکیده
منابع مشابه
Co-regular Spaces and Genus One Curves
Some examples of coregular spaces were mentioned last time binary quadratic forms, binary cubic forms etc. Clearly, any pre-homogeneous space is a vector space. Coregular spaces were first classified by Littelman (1989) for semisimple irreducible representations; there are around 50 of them including infinite families. A lot of these spaces come from Vinberg theory, something that’ll be discuss...
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Let X be a nonsingular projective curve of genus one defined over an algebraically closed field of characteristic 0. Let D be a divisor ofX of degree n > 1 and let O be a (closed) point ofX. As is well known, there exists a unique morphism φD,O : X → X such that φD,O(P ) = Q if and only if the divisor nP −D−O+Q is principal. Our main result is a simple explicit description of the map φD,O in te...
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We present explicit models for non-elliptic genus one Shimura curves X0(D, N) with Γ0(N)-level structure arising from an indefinite quaternion algebra of reduced discriminant D, and Atkin-Lehner quotients of them. In addition, we discuss and extend Jordan’s work [10, Ch. III] on points with complex multiplication on Shimura curves.
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ژورنال
عنوان ژورنال: Cambridge Journal of Mathematics
سال: 2016
ISSN: 2168-0930,2168-0949
DOI: 10.4310/cjm.2016.v4.n1.a1