Trace maps in motivic homotopy and local terms
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2020
- DOI:
- 10.48550/arXiv.2010.09292
- arXiv:
- arXiv:2010.09292
- Bibcode:
- 2020arXiv201009292J
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - K-Theory and Homology;
- 14F42;
- 14N10;
- 19E15
- E-Print:
- doi:10.1090/btran/169