Papers › Bézoutians and the 𝔸¹-degree
Bézoutians and the 𝔸¹-degree
Thomas Brazelton, Stephen McKean, Sabrina Pauli
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We prove that both the local and global 𝔸¹-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 𝔸¹-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.
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