Bézoutians and the $\mathbb{A}^1$-degree
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916164413685760 |
|---|---|
| author | Brazelton, Thomas McKean, Stephen Pauli, Sabrina |
| author_facet | Brazelton, Thomas McKean, Stephen Pauli, Sabrina |
| contents | 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 Bézoutian. In particular, we show that the Bézoutian 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_16614 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Bézoutians and the $\mathbb{A}^1$-degree Brazelton, Thomas McKean, Stephen Pauli, Sabrina Algebraic Geometry Commutative Algebra Algebraic Topology 14F42, 15A63 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 Bézoutian. In particular, we show that the Bézoutian 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. |
| title | Bézoutians and the $\mathbb{A}^1$-degree |
| topic | Algebraic Geometry Commutative Algebra Algebraic Topology 14F42, 15A63 |
| url | https://arxiv.org/abs/2103.16614 |