Fourier-stable subrings in the Chow rings of abelian varieties

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dc.creatorPolishchuk, Alexander
dc.date2007-05-05
dc.date2008-07-17
dc.date.accessioned2026-07-07T09:50:33Z
dc.date.available2026-07-07T09:50:33Z
dc.descriptionWe study subrings in the Chow ring $\CH^*(A)_{\Bbb Q}$ 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 $\leq 1$ one gets such a subring. We also show how to construct finite-dimensional Fourier-stable subrings in $\CH^*(A)_{\Bbb Q}$. Another result concerns the relation between the Pontryagin product and the usual product on the $\CH^*(A)_{\Bbb Q}$. 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 $\CH^*(A)_{\Bbb Q}$.
dc.description8 pages, in v.2 the order of the differential operator given by the product is computed exactly, v.3 minor typos corrected
dc.identifierhttps://arxiv.org/abs/0705.0772
dc.identifierhttp://arxiv.org/abs/0705.0772
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164976
dc.subjectAlgebraic Geometry
dc.titleFourier-stable subrings in the Chow rings of abelian varieties
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