A new discriminant algebra construction
Owen Biesel, Alberto Gioia · Documenta Mathematica · 2016
A discriminant algebra operation sends a commutative ring R and an R -algebra A of rank n to an R -algebra \Delta _A/R of rank 2 with the same discriminant bilinear form. Constructions of discriminant algebra operations have been put forward by Rost, Deligne, and Loos. We present a simpler and more explicit construction that does not break down into cases based on the parity of n . We then prove properties of this construction, and compute some examples explicitly.