A new discriminant algebra construction

  • Owen Biesel

    Mathematisch Instituut
  • Alberto Gioia

    Niels Bohrweg 1 Leiden University The Netherlands
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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.

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

DOI 10.4171/DM/552