论文标题
阿贝尔表面的示例失败了局部全球原理
Examples of abelian surfaces failing the local-global principle for isogenies
论文作者
论文摘要
我们提供了在数字字段上的Abelian表面$ k $的例子，这些数字的减少几乎所有优质的素质都具有Prime Grime $ \ Ell $ Rational的同一基础，而在残留领域上，但本身不承认$ K $ - 理性的$ \ ell $ iSGENY。这是基于库里南和萨瑟兰的作品。当$ k = \ mathbb {q} $时，我们确定某些权重 - $ 2 $ newforms $ f $带有二次傅立叶系数，其与模块化的Abelian相关的Abelian Surfaces $ a_f $表现出了类似于iSogen的局部全球原则的失败。
We provide examples of abelian surfaces over number fields $K$ whose reductions at almost all good primes possess an isogeny of prime degree $\ell$ rational over the residue field, but which themselves do not admit a $K$-rational $\ell$-isogeny. This builds on work of Cullinan and Sutherland. When $K=\mathbb{Q}$, we identify certain weight-$2$ newforms $f$ with quadratic Fourier coefficients whose associated modular abelian surfaces $A_f$ exhibit such a failure of a local-global principle for isogenies.
