Biesel, Owen; Gioia, Alberto

A new discriminant algebra construction

Doc. Math., J. DMV 21, 1051-1088 (2016)


Summary: 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.

Mathematics Subject Classification

13B02, 14B25, 11R11, 13B40, 13C10


discriminant algebra, discriminant form, algebra of finite rank, étale algebra, polynomial law