Torsion Motives

Vishik, Alexander

Abstract

In this paper we study Chow motives whose identity map is killed by a natural number. Examples of such objects were constructed by Gorchinskiy-Orlov [10]. We introduce various invariants of torsion motives, in particular, the p-level. We show that this invariant bounds from below the dimension of the variety a torsion motive M is a direct summand of and imposes restrictions on motivic and singular cohomology of M . We study in more details the p-torsion motives of surfaces, in particular, the Godeaux torsion motive. We show that such motives are in 1-to-1 correspondence with certain Rost cycle submodules of free modules over H∗et. This description is parallel to that of mod-p reduced motives of curves.

Citation

Vishik, A. (2023). Torsion Motives. International Mathematics Research Notices, 2023(23), 20252–20295. https://doi.org/10.1093/imrn/rnad056

• Journal Article Type: Article
• Acceptance Date: Feb 20, 2023
• Online Publication Date: Mar 29, 2023
• Publication Date: 2023-12
• Deposit Date: Mar 18, 2023
• Publicly Available Date: Mar 30, 2024
• Journal: International Mathematics Research Notices
• Print ISSN: 1073-7928
• Electronic ISSN: 1687-0247
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 2023
• Issue: 23
• Pages: 20252–20295
• DOI: https://doi.org/10.1093/imrn/rnad056
• Keywords: General Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/18595054
• Publisher URL: https://academic.oup.com/imrn/article/2023/23/20252/7093391