A classical proof that the algebraic homotopy class of a rational function is the residue pairing

DOI10.1016/j.laa.2019.12.041zbMath1437.14030arXiv1602.08129OpenAlexW3005773402MaRDI QIDQ2306300

Kirsten Wickelgren, Jesse Leo Kass

Publication date: 20 March 2020

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.08129

zbMATH Keywords

rational functionBézout matrixmotivic homotopy theoryresidue pairingdegree map$\mathbb{A}^1$-degree

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Degree, winding number (55M25) Motivic cohomology; motivic homotopy theory (14F42)

Related Items (6)

Arithmetic inflection formulae for linear series on hyperelliptic curves ⋮ On the EKL-degree of a Weyl cover ⋮ The class of Eisenbud-Khimshiashvili-Levine is the local \(\mathbb{A}^1\)-Brouwer degree ⋮ Morel homotopy modules and Milnor-Witt cycle modules ⋮ An introduction to \(\mathbb{A}^1\)-enumerative geometry. Based on lectures by Kirsten Wickelgren delivered at the LMS-CMI research school ``Homotopy theory and arithmetic geometry -- motivic and Diophantine aspects ⋮ An arithmetic count of the lines meeting four lines in 𝐏³

Cites Work

• Singularities of differentiable maps, Volume 1. Classification of critical points, caustics and wave fronts. Transl. from the Russian by Ian Porteous, edited by V. I. Arnol'd
• Motivic homotopy theory
• An algebraic formula for the degree of a \(C^\infty\) map germ. Sur une inegalite a la Minkowski pour les multiplicites
• The class of Eisenbud-Khimshiashvili-Levine is the local \(\mathbb{A}^1\)-Brouwer degree
• A polynomial approach to linear algebra
• Homotopy classes of rational functions
• The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations
• An algebraic approach to the topological degree of a smooth map
• Algebraic homotopy classes of rational functions
• Algorithms in real algebraic geometry
• \(\mathbb{A}^1\)-homotopy theory of schemes
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