Grothendieck groups of categories of abelian varieties

Ari Shnidman

doi:10.1007/s40879-017-0159-z

Grothendieck groups of categories of abelian varieties

Ari Shnidman^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	507-519
Number of pages	13
Journal	European Journal of Mathematics
Volume	3
Issue number	3
DOIs	https://doi.org/10.1007/s40879-017-0159-z
State	Published - 1 Sep 2017
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2017, Springer International Publishing AG.

Keywords

Abelian varieties
Elliptic curves
Grothendieck groups

Access to Document

10.1007/s40879-017-0159-z

Cite this

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AB - 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.

KW - Abelian varieties

KW - Elliptic curves

KW - Grothendieck groups

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Grothendieck groups of categories of abelian varieties

Abstract

Bibliographical note

Keywords

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