A note on the Grothendieck group of an abelian variety

2018/05/30 by Shahram Biglari, Biglari, Shahram
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1805.12095

Abstract

We reformulate a conjecture of Beauville on algebraic cycles on an abelian variety in terms of certain compatibility and vanishings of some naturally defined filtrations on the Grothendieck group of the abelian variety.

Related

• Grothendieck groups of categories of abelian varieties
• Coniveau and the Grothendieck group of varieties
• Filtrations of the Chow group of zero-cycles on abelian varieties and behavior under isogeny
• Cycle conjectures and birational invariants over finite fields
• A Filtration of the Chow Group of Zero-Cycles for a Product of Curves and an Abelian Variety