Abstract We equate various Euler classes of algebraic vector bundles, including those [12] and one suggested by M. J. Hopkins, A. Raksit, J.-P. Serre. establish integrality results for this class give formulas local indices at isolated zeros, both in terms the six-functors formalism coherent sheaves as an explicit recipe commutative algebra Scheja Storch. As application, we compute enriched bil...