This paper is a work in progress on Bloch's conjecture asserting the vanishing of the Pontryagin product of a $ p $ codimensional cycle on an abelian variety by $ p+1 $ zero cycles of degree zero. We prove an infinitesimal version of the conjecture and we discuss, in particular, the case of $ 3 $ dimensional cycles.

Marini, G. (2021). An infinitesimal approach to the study of cycles on abelian varieties. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 23(4) [10.1142/S0219199720500418].

An infinitesimal approach to the study of cycles on abelian varieties

Marini Giambattista
2021-01-01

Abstract

This paper is a work in progress on Bloch's conjecture asserting the vanishing of the Pontryagin product of a $ p $ codimensional cycle on an abelian variety by $ p+1 $ zero cycles of degree zero. We prove an infinitesimal version of the conjecture and we discuss, in particular, the case of $ 3 $ dimensional cycles.
2021
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
Abelian variety; algebraic cycles; Bloch's conjecture; Beauville's conjecture; Chow group; Chow ring; rational equivalence
Marini, G. (2021). An infinitesimal approach to the study of cycles on abelian varieties. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 23(4) [10.1142/S0219199720500418].
Marini, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/262287
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