Grothendieck groups of categories of abelian varieties

2017/01/13 by Shnidman, Ari
#11G10 #14K99 #19A99 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1701.03744

Abstract

We compute the Grothendieck group of the category of abelian varieties over an algebraically closed field k. We also compute the Grothendieck group of the category of A-isotypic abelian varieties, for any simple abelian variety A, assuming k has characteristic 0, and for any elliptic curve A in any characteristic.

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