Abstract
Using the localization property, we construct triangulated categories of motives over quasi-projective $T$-schemes for any coefficient where $T$ is a noetherian separated scheme, and we prove the Grothendieck six operations formalism. We also construct integral étale realization of motives.
Acknowledgment
The author is grateful to Martin Olsson for helpful conversations. The author is grateful to Adeel Khan for indicating that orientation for ${\rm DM}^{loc}(-,\Lambda)$ is needed. Section 10 is obtained from a conversation with him. Most part of this paper was written when the author was a graduate student in University of California, Berkeley.
Citation
Doosung Park. "Construction of triangulated categories of motives using the localization property." Kodai Math. J. 44 (2) 195 - 264, June 2021. https://doi.org/10.2996/kmj44201
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