Trace maps in motivic homotopy and local terms
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- by Fangzhou Jin
- Trans. Amer. Math. Soc. Ser. B 11 (2024), 215-247
- DOI: https://doi.org/10.1090/btran/169
- Published electronically: January 26, 2024
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Abstract:
We define a trace map for every cohomological correspondence in the motivic stable homotopy category over a general base scheme, which takes values in the twisted bivariant groups. Local contributions to the trace map give rise to quadratic refinements of the classical local terms, and some $\mathbb {A}^1$-enumerative invariants, such as the local $\mathbb {A}^1$-Brouwer degree and the Euler class with support, can be interpreted as local terms. We prove an analogue of a theorem of Varshavsky, which states that for a contracting correspondence, the local terms agree with the naive local terms.References
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Bibliographic Information
- Fangzhou Jin
- Affiliation: School of Mathematical Sciences, Tongji University, Siping Road 1239, 200092 Shanghai, People’s Republic of China
- MR Author ID: 1167688
- ORCID: 0000-0003-3190-5526
- Email: fangzhoujin@tongji.edu.cn
- Received by editor(s): August 21, 2022
- Received by editor(s) in revised form: August 30, 2023
- Published electronically: January 26, 2024
- Additional Notes: The author was supported by the National Key Research and Development Program of China Grant Nr.2021YFA1001400, the National Natural Science Foundation of China Grant Nr.12101455, the Fundamental Research Funds for the Central Universities, and the ERC Project-QUADAG, which has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement Nr.832833).
- © Copyright 2024 by the author under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License (CC BY NC ND 4.0)
- Journal: Trans. Amer. Math. Soc. Ser. B 11 (2024), 215-247
- MSC (2020): Primary 14F42; Secondary 14N10, 19E15
- DOI: https://doi.org/10.1090/btran/169
- MathSciNet review: 4695508