E-motives and motivic stable homotopy
Abstract
We introduce in this work the notion of the category of pure $\mathbf{E}$-Motives, where $\mathbf{E}$ is a motivic strict ring spectrum and construct twisted $\mathbf{E}$-cohomology by using six functors formalism of J. Ayoub. In particular, we construct the category of pure Chow-Witt motives $CHW(k)_{\mathbb{Q}}$ over a field $k$ and show that this category admits a fully faithful embedding into the geometric stable $\mathbb{A}^1$-derived category $D_{\mathbb{A}^1,gm}(k)_{\mathbb{Q}}$.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2017
- DOI:
- 10.48550/arXiv.1704.07672
- arXiv:
- arXiv:1704.07672
- Bibcode:
- 2017arXiv170407672N
- Keywords:
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- Mathematics - K-Theory and Homology;
- Mathematics - Algebraic Geometry;
- Mathematics - Algebraic Topology
- E-Print:
- First replacement of arXiv:1204.2787v11 [math.AG]