论文标题
积分傅立叶变换和Abelian品种上一循环的整体猪头猜想
Integral Fourier transforms and the integral Hodge conjecture for one-cycles on abelian varieties
论文作者
论文摘要
我们证明了在主要极化的复杂的阿贝尔（Abelian）品种上，其最小类是代数。尤其是，在复数上平滑投射曲线的雅各布人的任何产物都可以满足一循环的整体猪头猜想。主要成分是将傅立叶变换升至整体食物基团。同样，我们证明了在有限生成的磁场的可分离闭合上，在适当的紧凑型曲线的雅各布上的一个循环的泰特猜想。此外，满足这种猜想的Abelian品种在其模量空间中是密集的。
We prove the integral Hodge conjecture for one-cycles on a principally polarized complex abelian variety whose minimal class is algebraic. In particular, any product of Jacobians of smooth projective curves over the complex numbers satisfies the integral Hodge conjecture for one-cycles. The main ingredient is a lift of the Fourier transform to integral Chow groups. Similarly, we prove the integral Tate conjecture for one-cycles on the Jacobian of a proper curve of compact type over the separable closure of a finitely generated field. Furthermore, abelian varieties satisfying such a conjecture are dense in their moduli space.
