A new discriminant algebra construction

  • Owen Biesel

    Mathematisch Instituut
  • Alberto Gioia

    Niels Bohrweg 1 Leiden University The Netherlands
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Abstract

A discriminant algebra operation sends a commutative ring RR and an RR-algebra AA of rank nn to an RR-algebra Δ\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 nn. We then prove properties of this construction, and compute some examples explicitly.

Cite this article

Owen Biesel, Alberto Gioia, A new discriminant algebra construction. Doc. Math. 21 (2016), pp. 1051–1088

DOI 10.4171/DM/552