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June 2021 Construction of triangulated categories of motives using the localization property
Doosung Park
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Kodai Math. J. 44(2): 195-264 (June 2021). DOI: 10.2996/kmj44201

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

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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

Information

Received: 22 August 2019; Revised: 9 October 2020; Published: June 2021
First available in Project Euclid: 29 June 2021

Digital Object Identifier: 10.2996/kmj44201

Subjects:
Primary: 14F42
Secondary: 19E15

Rights: Copyright © 2021 Tokyo Institute of Technology, Department of Mathematics

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Vol.44 • No. 2 • June 2021
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