Details
Original language | English |
---|---|
Pages (from-to) | 1188-1213 |
Number of pages | 26 |
Journal | Compositio mathematica |
Volume | 159 |
Issue number | 6 |
Early online date | 15 May 2023 |
Publication status | Published - 2023 |
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.
Keywords
- Chow rings, cohomology, integral Hodge conjecture, subvarieties of abelian varieties
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Compositio mathematica, Vol. 159, No. 6, 2023, p. 1188-1213.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Integral Fourier transforms and the integral Hodge conjecture for one-cycles on abelian varieties
AU - Beckmann, Thorsten
AU - De Gaay Fortman, Olivier
N1 - Funding Information: The first author was supported by the IMPRS program of the Max–Planck Society. The second author was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754362.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - Chow rings
KW - cohomology
KW - integral Hodge conjecture
KW - subvarieties of abelian varieties
UR - http://www.scopus.com/inward/record.url?scp=85160861532&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2202.05230
DO - 10.48550/arXiv.2202.05230
M3 - Article
AN - SCOPUS:85160861532
VL - 159
SP - 1188
EP - 1213
JO - Compositio mathematica
JF - Compositio mathematica
SN - 0010-437X
IS - 6
ER -