Borel-Moore motivic homology and weight structure on mixed motives
Fangzhou Jin
TL;DR
This paper establishes a connection between Borel-Moore motivic homology and the weight structure on mixed motives, identifying the heart of the structure with a known category of Chow motives, thus resolving a key question.
Contribution
It defines and studies Borel-Moore motivic homology to identify the heart of the weight structure with Chow motives, providing a significant link in the theory of mixed motives.
Findings
Identified the heart of Bondarko-Hébert's weight structure with Chow motives.
Established functorial properties of Borel-Moore motivic homology.
Answered a longstanding question in the theory of mixed motives.
Abstract
By defining and studying functorial properties of the Borel-Moore motivic homology, we identify the heart of Bondarko-H\'ebert's weight structure on Beilinson motives with Corti-Hanamura's category of Chow motives over a base, therefore answering a question of Bondarko.
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