B\'ezoutians and the $\mathbb{A}^1$-degree

Autor:	Brazelton, Thomas, McKean, Stephen, Pauli, Sabrina
Rok vydání:	2021
Předmět:	Mathematics - Algebraic Geometry Mathematics - Commutative Algebra Mathematics - Algebraic Topology 14F42 15A63
Zdroj:	Alg. Number Th. 17 (2023) 1985-2012
Druh dokumentu:	Working Paper
DOI:	10.2140/ant.2023.17.1985
Popis:	We prove that both the local and global $\mathbb{A}^1$-degree of an endomorphism of affine space can be computed in terms of the multivariate B\'ezoutian. In particular, we show that the B\'ezoutian bilinear form, the Scheja--Storch form, and the $\mathbb{A}^1$-degree for complete intersections are isomorphic. Our global theorem generalizes Cazanave's theorem in the univariate case, and our local theorem generalizes Kass--Wickelgren's theorem on EKL forms and the local degree. This result provides an algebraic formula for local and global degrees in motivic homotopy theory. Comment: Fixed a small typo
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2103.16614 Zobrazit plný text záznamu View this record from Arxiv