Grothendieck groups of categories of abelian varieties

Ari Shnidman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageAmerican English
Pages (from-to)507-519
Number of pages13
JournalEuropean Journal of Mathematics
Volume3
Issue number3
DOIs
StatePublished - 1 Sep 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017, Springer International Publishing AG.

Keywords

  • Abelian varieties
  • Elliptic curves
  • Grothendieck groups

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