The Voevodsky motive of a rank one semiabelian variety

zbMATH Open1286.14001arXiv1307.4785MaRDI QIDQ2844762

Stephen Enright-Ward

Publication date: 19 August 2013

Abstract: Over a perfect field k, let G be an extension of an abelian variety by the multiplicative group $G_m$. We compute the motive of G in Voevodsky's category of etale motivic complexes with rational coefficients. The result is a decomposition similar to the classical decomposition of the Chow motive of an abelian variety obtained by Deninger/Murre, Kuennemann, Shermenev and Scholl, and other authors.

Full work available at URL: https://arxiv.org/abs/1307.4785

zbMATH Keywords

symmetric powereffective Chow motiveVoevodsky category of étale motivic complexes

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Drinfel'd modules; higher-dimensional motives, etc. (11G09) Abelian varieties and schemes (14K99)

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