PreprintarXiv licencearXiv
Isotropic localizations of mixed initial motives
Abstract
In this paper, we define the triangulated category of initial motives, which contains, for example, all motives of projective homogeneous varieties for semisimple algebraic groups of inner type. By analyzing its Chow weight structure, we prove that the family of isotropic localizations indexed by finitely generated extensions of the base field is conservative and Pic-injective on initial motives. This result provides an extension, in the mixed setting, of the work of Quéguiner-Mathieu and the first author on higher Tate traces of Chow motives.
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BibTeX
@misc{clercq2026isotropic,
title = {{Isotropic localizations of mixed initial motives}},
author = {Charles De Clercq and Fabio Tanania},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37862},
eprint = {2609.37862},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37862},
}
RIS
TY - UNPB
TI - Isotropic localizations of mixed initial motives
AU - Charles De Clercq
AU - Fabio Tanania
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37862
UR - https://arxiv.org/abs/2609.37862
AB - In this paper, we define the triangulated category of initial motives, which contains, for example, all motives of projective homogeneous varieties for semisimple algebraic groups of inner type. By analyzing its Chow weight structure, we prove that the family of isotropic localizations indexed by finitely generated extensions of the base field is conservative and Pic-injective on initial motives. This result provides an extension, in the mixed setting, of the work of Quéguiner-Mathieu and the first author on higher Tate traces of Chow motives.
ER -