Inhaltszusammenfassung

Spitzweck's representation theorem states that the triangulated category of mixed Tate motives, $DMT(k)$, over a perfect field $k$ is equivalent to the bounded homotopy category of finite $mathcal{N}(k)$-cell modules, $mathcal{KCM}_{mathcal{N}(k)}^f$, where $mathcal{N}(k)$ is the cycle algebra over $k$. The category $DMT(k)$ is a full triangulated subcategory of the category of mixed Artin-Tate motives, $DMAT(k)$. For a number field $k$, we construct a category of cell modules that is equival...Spitzweck's representation theorem states that the triangulated category of mixed Tate motives, $DMT(k)$, over a perfect field $k$ is equivalent to the bounded homotopy category of finite $mathcal{N}(k)$-cell modules, $mathcal{KCM}_{mathcal{N}(k)}^f$, where $mathcal{N}(k)$ is the cycle algebra over $k$. The category $DMT(k)$ is a full triangulated subcategory of the category of mixed Artin-Tate motives, $DMAT(k)$. For a number field $k$, we construct a category of cell modules that is equivalent to $DMAT(k)$ and restricts to the equivalence given by Spitzweck's representation theorem. Furthermore, $DMT(k)$ and $DMAT(k)$ carry non-degenerate t-structures whose hearts are the Tannakian categories $MT(k)$ respectively $MAT(k)$. We compute the Tannaka group of $MAT(k)$ as the semi-direct product of the absolute Galois group of $k$ and the Tannaka group of $MT(bar{k})$.» weiterlesen» einklappen

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DDC Sachgruppe:
Mathematik