Geodesic
The trace of the local $\mathbb{A}^1$-degree
Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 243-255.

Voir la notice de l'article provenant de la source International Press of Boston

We prove that the local $\mathbb{A}^1$-degree of a polynomial function at an isolated zero with finite separable residue field is given by the trace of the local $\mathbb{A}^1$-degree over the residue field. This fact was originally suggested by Morel’s work on motivic transfers, and by Kass and Wickelgren’s work on the Scheja–Storch bilinear form. As a corollary, we generalize a result of Kass and Wickelgren relating the Scheja–Storch form and the local $\mathbb{A}^1$-degree.
DOI : 10.4310/HHA.2021.v23.n1.a13
Classification : 14F42, 55M25, 55P42
Keywords: motivic, homotopy, enumerative, geometry, trace, degree 
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Thomas Brazelton; Robert Burklund; Stephen McKean; Michael Montoro; Morgan Opie. The trace of the local $\mathbb{A}^1$-degree. Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 243-255. doi : 10.4310/HHA.2021.v23.n1.a13. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n1.a13/

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