Fourier-stable Subrings in the Chow Rings of Abelian Varieties
نویسنده
چکیده
We study subrings in the Chow ring CH∗(A)Q of an abelian variety A, stable under the Fourier transform with respect to an arbitrary polarization. We prove that by taking Pontryagin products of classes of dimension ≤ 1 one gets such a subring. We also show how to construct finite-dimensional Fourier-stable subrings in CH∗(A)Q. Another result concerns the relation between the Pontryagin product and the usual product on the CH∗(A)Q. We prove that the operator of the usual product with a cycle is a differential operator with respect to the Pontryagin product and compute its order in terms of the Beauville’s decomposition of CH∗(A)Q.
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