JournalsdmVol. 20pp. 807–858

On the motive of a commutative algebraic group

  • Stephen Enright-Ward

    Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstraße 1, 79104 Freiburg im Breisgau, Germany

  • Giuseppe Ancona

    Universität Duisburg-Essen, Thea-Leymann-Straße 9, 45127 Essen, Germany
    ORCID

  • Annette Huber

    Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstraße 1, 79104 Freiburg im Breisgau, Germany
On the motive of a commutative algebraic group cover
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Abstract

We prove a canonical Künneth decomposition for the motive of a commutative group scheme over a field. Moreover, we show that this decomposition behaves under the group law just as in cohomology. We also deduce applications of the decomposition to the existence of a weight filtration, computation of any Weil cohomology theory and study of 1-motives.

Cite this article

Stephen Enright-Ward, Giuseppe Ancona, Annette Huber, On the motive of a commutative algebraic group. Doc. Math. 20 (2015), pp. 807–858

DOI 10.4171/DM/506