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- Title
Integral Fourier transforms and the integral Hodge conjecture for one-cycles on abelian varieties.
- Authors
Beckmann, Thorsten; de Gaay Fortman, Olivier
- Abstract
We prove the integral Hodge conjecture for one-cycles on a principally polarized complex abelian variety whose minimal class is algebraic. In particular, the Jacobian of a smooth projective curve 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 smooth projective curve over the separable closure of a finitely generated field. Furthermore, abelian varieties satisfying such a conjecture are dense in their moduli space.
- Subjects
FOURIER integrals; INTEGRAL transforms; ABELIAN varieties; ALGEBRAIC cycles; FOURIER transforms; LOGICAL prediction; COMPLEX numbers
- Publication
Compositio Mathematica, 2023, Vol 159, Issue 6, p1188
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X23007133