Discrete tomography and Hodge cycles
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概要
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We study a problem in discrete tomography on the free abelian group of rank $n$ through the theory of distributions on the $n$-dimensional torus, and show that there is an intimate connection between the problem and the study of the Hodge cycles on abelian varieties of CM-type. This connection enables us to apply our results in tomography to obtain several infinite families of abelian varieties for which the Hodge conjecture hold.
- 東北大学の論文
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関連論文
- Discrete Tomography through Distribution Theory
- Hodge cycles on abelian varieties associated to the complete binary trees
- Hodge Cycles on Abelian Varieties with Complex Multiplication by Cyclic CM-Fields
- Geometric analogue of the Mumford-Tate Conjecture for stably non-degenerate abelian varieties (A note on Mustafin's paper)
- Discrete tomography and Hodge cycles
- On the General Hodge Conjecture for Abelian Varieties of CM-type