Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for Abelian varieties

Vial C (2020)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 21(Issue Special): 1411-1451.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Abstract / Bemerkung
We prove Bloch's conjecture for correspondences on powers of complex Abelian varieties, that are "generically defined". As an application we establish vanishing results for (skew-)symmetric cycles on powers of Abelian varieties and we address a question of Voisin concerning (skew-)symmetric cycles on powers of K3 surfaces in the case of Kummer surfaces. We also prove Bloch's conjecture in the following situation. Let gamma be a correspondence between two Abelian varieties A and B that can be written as a linear combination of products of symmetric divisors. Assume that A is isogenous to the product of an Abelian variety of totally real type with the power of an Abelian surface. We show that gamma satisfies the conclusion of Bloch's conjecture. A key ingredient consists in establishing a strong form of the generalized Hodge conjecture for Hodge sub-structures of the cohomology of A that arise as sub-representations of the Lefschetz group of A. As a by-product of our method, we use a strong form of the generalized Hodge conjecture established for powers of Abelian surfaces to show that every finite-order symplectic automorphism of a generalized Kummer variety acts as the identity on the zero-cycles.
Erscheinungsjahr
2020
Zeitschriftentitel
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Band
21
Ausgabe
Issue Special
Seite(n)
1411-1451
ISSN
0391-173X
eISSN
2036-2145
Page URI
https://pub.uni-bielefeld.de/record/2952145

Zitieren

Vial C. Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for Abelian varieties. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 2020;21(Issue Special):1411-1451.
Vial, C. (2020). Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for Abelian varieties. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, 21(Issue Special), 1411-1451. https://doi.org/10.2422/2036-2145.201811_010
Vial, C. (2020). Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for Abelian varieties. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 21, 1411-1451.
Vial, C., 2020. Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for Abelian varieties. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, 21(Issue Special), p 1411-1451.
C. Vial, “Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for Abelian varieties”, Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, vol. 21, 2020, pp. 1411-1451.
Vial, C.: Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for Abelian varieties. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 21, 1411-1451 (2020).
Vial, Charles. “Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for Abelian varieties”. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 21.Issue Special (2020): 1411-1451.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar