Integral Fourier transforms and the integral Hodge conjecture for one-cycles on abelian varieties

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Thorsten Beckmann
  • Olivier De Gaay Fortman

Organisationseinheiten

Externe Organisationen

  • Max-Planck-Institut für Mathematik
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Details

OriginalspracheEnglisch
Seiten (von - bis)1188-1213
Seitenumfang26
FachzeitschriftCompositio mathematica
Jahrgang159
Ausgabenummer6
Frühes Online-Datum15 Mai 2023
PublikationsstatusVeröffentlicht - 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.

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Integral Fourier transforms and the integral Hodge conjecture for one-cycles on abelian varieties. / Beckmann, Thorsten; De Gaay Fortman, Olivier.
in: Compositio mathematica, Jahrgang 159, Nr. 6, 2023, S. 1188-1213.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Beckmann T, De Gaay Fortman O. Integral Fourier transforms and the integral Hodge conjecture for one-cycles on abelian varieties. Compositio mathematica. 2023;159(6):1188-1213. Epub 2023 Mai 15. doi: 10.48550/arXiv.2202.05230, 10.1112/S0010437X23007133
Beckmann, Thorsten ; De Gaay Fortman, Olivier. / Integral Fourier transforms and the integral Hodge conjecture for one-cycles on abelian varieties. in: Compositio mathematica. 2023 ; Jahrgang 159, Nr. 6. S. 1188-1213.
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