@article{Brazelton_McKean_2023, title={Lifts, transfers, and degrees of univariate maps}, volume={129}, url={https://www.mscand.dk/article/view/134457}, DOI={10.7146/math.scand.a-134457}, abstractNote={<p>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.</p>}, number={1}, journal={MATHEMATICA SCANDINAVICA}, author={Brazelton, Thomas and McKean, Stephen}, year={2023}, month={Feb.} }