M. Levine proved an enrichment of the classical Riemann-Hurwitz formula to an equality in the Grothendieck-Witt group of quadratic forms. In its strongest form, Levine's theorem includes a technical hypothesis on ramification relevant in positive characteristic. We consider wild ramification at points whose residue fields are non-separable extensions of the ground field k. We show an analogous Riemann-Hurwitz formula, and consider an example suggested by S. Saito.Date: December 11, 2018.
We show the A 1 -Euler characteristic of a smooth, projective scheme over a characteristic 0 field is represented by its Hochschild complex together with a canonical bilinear form, and give an exposition of the compactly supported A 1 -Euler characteristic χ cA 1 : K 0 (Var k ) GW(k) from the Grothendieck group of varieties to the Grothendieck-Witt group of bilinear forms. We also provide example computations.
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