Euler Classes of algebraic vector bundles

A^1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections

We equate various algebraic vector bundles, including those of [bm, kw, djk, and one suggested by m. j. hopkins, a. raksit, and j.-p. serre.We establish integrality results for this vector bundle, and give formulas for local indices at isolated zeros, both in terms of 6-functor formalism of coherent sheaves and as an explicit recipe in commutative algebra of scheja and storch.