Trace maps in motivic homotopy and local terms
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866913286998458368 |
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| author | Jin, Fangzhou |
| author_facet | Jin, Fangzhou |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_09292 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Trace maps in motivic homotopy and local terms Jin, Fangzhou Algebraic Geometry K-Theory and Homology 14F42, 14N10, 19E15 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. |
| title | Trace maps in motivic homotopy and local terms |
| topic | Algebraic Geometry K-Theory and Homology 14F42, 14N10, 19E15 |
| url | https://arxiv.org/abs/2010.09292 |