摘要翻译:
本文给出了一种确定模阿贝尔曲面A_F$的主极化同构类的方法,该模阿贝尔曲面A_F$带有四元数乘法,且不带复乘法。我们给出了一个具有四元数乘法的$A_F$的例子,在数值上我们找到了一条曲线$C$,它的雅可比系数是$A_F$直到数值逼近,并且证明了它具有四元数乘法并且与$A_F$是等价的。
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英文标题:
《Genus two curves with quaternionic multiplication and modular jacobian》
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作者:
Josep Gonzalez, Jordi Guardia
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Number Theory 数论
分类描述:Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数,丢番图方程,解析数论,代数数论,算术几何,伽罗瓦理论
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces $A_f$ with quaternionic multiplication attached to a normalized newform $f$ without complex multiplication. We include an example of $A_f$ with quaternionic multiplication for which we find numerically a curve $C$ whose Jacobian is $A_f$ up to numerical approximation, and we prove that it has quaternionic multiplication and is isogenous to $A_f$.
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PDF链接:
https://arxiv.org/pdf/0805.1302