Lifts, transfers, and degrees of univariate maps


  • Thomas Brazelton
  • Stephen McKean



One can compute the local $\mathbb{A}^1$-degree at points with separable residue field by base changing, working rationally, and post-composing with the field trace. We show that for endomorphisms of the affine line, one can compute the local $\mathbb{A}^1$-degree at points with inseparable residue field by taking a suitable lift of the polynomial and transferring its local degree. We also discuss the general set-up and strategy in terms of the six functor formalism. As an application, we show that trace forms of number fields are local $\mathbb{A}^1$-degrees.


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How to Cite

Brazelton, T., & McKean, S. (2023). Lifts, transfers, and degrees of univariate maps. MATHEMATICA SCANDINAVICA, 129(1).