Corpus ID: 208006103

$\mathbb{A}^{1}$-Local Degree via Stacks

@article{Kobin2019mathbbA1LocalDV,
  title={\$\mathbb\{A\}^\{1\}\$-Local Degree via Stacks},
  author={Andrew Kobin and Libby Taylor},
  journal={arXiv: Algebraic Geometry},
  year={2019}
}
We extend results of Kass--Wickelgren to define an Euler class for a non-orientable (or non-relatively orientable) vector bundle on a smooth scheme, valued in the Grothendieck--Witt group of the ground field. We use a root stack construction to produce this Euler class and discuss its relation to other versions of an Euler class in $\mathbb{A}^{1}$-homotopy theory. This allows one to apply Kass--Wickelgren's technique for arithmetic enrichments of enumerative geometry to a larger class of… Expand
2 Citations
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